Alexander Merkurjev

Alexander Merkurjev is a professor of mathematics at the University of California, Los Angeles (UCLA). Born in 1955 (in what was then Leningrad, Soviet Union), he is renowned for his significant contributions to algebra, particularly in the areas of algebraic K-theory and Galois cohomology. Perhaps his most famous result—proved jointly with Andrei Suslin—is the Merkurjev–Suslin theorem, a foundational achievement in the theory of central simple algebras and the study of the Brauer group. He is also a Fellow of the American Mathematical Society.

All published works

Action	Title	Year	Authors
+ PDF Chat	The lifting problem for Galois representations	2025	Alexander Merkurjev Federico Scavia
+ PDF Chat	Galois representations modulo $p$ that do not lift modulo $p^2$	2024	Alexander Merkurjev Federico Scavia
+	Degenerate fourfold Massey products over arbitrary fields	2024	Alexander Merkurjev Federico Scavia
+ PDF Chat	Operations in connective K-theory	2023	Alexander Merkurjev Alexander Vishik
+ PDF Chat	Krull dimension of the negligible quotient in mod p cohomology of a finite group	2023	Matthew Gherman Alexander Merkurjev
+	The Massey Vanishing Conjecture for fourfold Massey products modulo 2	2023	Alexander Merkurjev Federico Scavia
+	On the Massey Vanishing Conjecture and Formal Hilbert 90	2023	Alexander Merkurjev Federico Scavia
+	Non-formality of Galois cohomology modulo all primes	2023	Alexander Merkurjev Federico Scavia
+ PDF Chat	Negligible degree two cohomology of finite groups	2022	Matthew Gherman Alexander Merkurjev
+	Classification of Special Reductive Groups	2022	Alexander Merkurjev
+	Indexes of generic Grassmannians for spin groups	2022	Nikita A. Karpenko Alexander Merkurjev
+	Poincaré duality for tautological Chern subrings of orthogonal grassmannians	2022	Nikita A. Karpenko Alexander Merkurjev
+	The Chow ring of the classifying space of the unitary group	2022	Nikita A. Karpenko Alexander Merkurjev
+	Degenerate fourfold Massey products over arbitrary fields	2022	Alexander Merkurjev Federico Scavia
+	Equivariant connective 𝐾-theory	2021	Nikita A. Karpenko Alexander Merkurjev
+	Connective $K$-theory and Adams operations	2021	Olivier Haution Alexander Merkurjev
+ PDF Chat	Additive operations between connective K-theory and Chow theory	2021	Alexander Merkurjev
+ PDF Chat	Invariants of algebraic tori of degree and weight 2	2021	Alexander Merkurjev Alexander Wertheim
+ PDF Chat	Maximal indexes of flag varieties for spin groups	2021	Rostislav Devyatov Nikita A. Karpenko Alexander Merkurjev
+	Connective K-theory and Adams operations	2020	Olivier Haution Alexander Merkurjev
+	Connective K-theory and Adams operations	2020	Olivier Haution Alexander Merkurjev
+	Operations in connective K-theory	2020	Alexander Merkurjev Alexander Vishik
+	Rationality Problem for Classifying Spaces of Spinor Groups	2019	Alexander Merkurjev
+ PDF Chat	The mathematics of Andrei Suslin	2019	Eric M. Friedlander Alexander Merkurjev
+	On a pairing for algebraic tori	2019	Alexander Merkurjev
+	VERSAL TORSORS AND RETRACTS	2019	Alexander Merkurjev
+ PDF Chat	Chow Filtration on Representation Rings of Algebraic Groups	2019	Nikita A. Karpenko Alexander Merkurjev
+ PDF Chat	The norm principle for type $D_n$ groups over complete discretely valued fields	2018	Nivedita Bhaskhar Vladimir Chernousov Alexander Merkurjev
+	Unramified degree three invariants for reductive groups of type A	2018	Alexander Merkurjev
+	Degree three unramified cohomology of adjoint semisimple groups	2017	Alexander Merkurjev
+	The norm principle for type $D_n$ groups over complete discretely valued fields	2017	Nivedita Bhaskhar Vladimir Chernousov Alexander Merkurjev
+ PDF Chat	On polynomially integrable convex bodies	2017	Alexander Koldobsky Alexander Merkurjev Vladyslav Yaskin
+ PDF Chat	Rost invariant of the center, revisited	2017	Skip Garibaldi Alexander Merkurjev
+ PDF Chat	Excellence of function fields of conics	2017	Alexander Merkurjev Jean-Pierre Tignol
+	Invariants of algebraic groups and retract rationality of classifying spaces	2017	Alexander Merkurjev
+	On polynomially integrable convex bodies	2017	Alexander Koldobsky Alexander Merkurjev Vladyslav Yaskin
+	The norm principle for type $D_n$ groups over complete discretely valued fields	2017	Nivedita Bhaskhar Vladimir Chernousov Alexander Merkurjev
+	On polynomially integrable convex bodies	2017	Alexander Koldobsky Alexander Merkurjev Vladyslav Yaskin
+ PDF Chat	Essential dimension	2016	Alexander Merkurjev
+	Degree three cohomological invariants of reductive groups	2016	Donald Joseph Laackman Alexander Merkurjev
+ PDF Chat	Motivic decomposition of compactifications of certain group varieties	2016	Nikita A. Karpenko Alexander Merkurjev
+	Cohomological invariants of central simple algebras	2016	Alexander Merkurjev
+	Unramified degree three invariants of reductive groups	2016	Alexander Merkurjev
+ PDF Chat	Degree three cohomological invariants of semisimple groups	2016	Alexander Merkurjev
+	Milnor′s Lemma, Newton′s Method, and Continued Fractions	2016	Boris M. Bekker О. А. Иванов Alexander Merkurjev
+	An algebraic identity and the Jacobi–Trudi formula	2016	Boris M. Bekker О. А. Иванов Alexander Merkurjev
+ PDF Chat	Weight two motivic cohomology of classifying spaces for semisimple groups	2016	Alexander Merkurjev
+	Excellence of function fields of conics	2015	Alexander Merkurjev Jean-Pierre Tignol
+ PDF Chat	Invariants of degree 3 and torsion in the Chow group of a versal flag	2015	Alexander Merkurjev Alexander Neshitov Kirill Zainoulline
+ PDF Chat	Motivic decomposition of certain special linear groups	2015	Alexander Merkurjev
+ PDF Chat	Suslin’s conjecture on the reduced Whitehead group of a simple algebra	2015	Alexander Merkurjev
+	Excellence of function fields of conics	2015	Alexander Merkurjev Jean-Pierre Tignol
+ PDF Chat	Hermitian forms over quaternion algebras	2014	Nikita A. Karpenko Alexander Merkurjev
+ PDF Chat	Essential dimension of spinor and Clifford groups	2014	Vladimir Chernousov Alexander Merkurjev
+	Quadratic Forms and Linear Algebraic Groups	2014	Detlev W. Hoffmann Alexander Merkurjev Jean-Pierre Tignol
+	Motivic decomposition of compactifications of certain group varieties	2014	Nikita A. Karpenko Alexander Merkurjev
+	Motivic decomposition of compactifications of certain group varieties	2014	Nikita A. Karpenko Alexander Merkurjev
+ PDF Chat	Cohomological invariants of algebraic tori	2013	Sam Blinstein Alexander Merkurjev
+	Essential dimension: a survey	2013	Alexander Merkurjev
+ PDF Chat	On standard norm varieties	2013	Nikita A. Karpenko Alexander Merkurjev
+	Algebra & Number Theory	2013	Sam Blinstein Alexander Merkurjev
+	Essential $$p$$ -dimension of split simple groups of type $$A_n$$	2012	Vladimir Chernousov Alexander Merkurjev
+	Generic values of quadratic forms and essential dimension	2012	Alexander Merkurjev
+	On standard norm varieties	2012	Nikita A. Karpenko Alexander Merkurjev
+ PDF Chat	Essential dimension of central simple algebras	2012	Sanghoon Baek Alexander Merkurjev
+	On standard norm varieties	2012	Nikita A. Karpenko Alexander Merkurjev
+ PDF Chat	A lower bound on the essential dimension of simple algebras	2010	Alexander Merkurjev
+	Motivic cohomology of the simplicial motive of a Rost variety	2010	Alexander Merkurjev Andrei Suslin
+	Essential 𝑝-dimension of 𝐏𝐆𝐋(𝐩²)	2010	Alexander Merkurjev
+	Adams Operations and the Brown-Gersten-Quillen Spectral Sequence	2010	Alexander Merkurjev
+	Quadratic Forms and Linear Algebraic Groups	2009	Detlev W. Hoffmann Alexander Merkurjev Jean-Pierre Tignol
+ PDF Chat	Invariants of simple algebras	2009	Sanghoon Baek Alexander Merkurjev
+	Algebraic groups, quadratic forms and related topics	2009	Vladimir Chernousov Alexander Merkurjev Zinovy Reichstein
+	Applications of the Milnor conjecture	2008	Richard Elman Nikita A. Karpenko Alexander Merkurjev
+	Bilinear and quadratic forms and algebraic extensions	2008	Richard Elman Nikita A. Karpenko Alexander Merkurjev
+	Homology and cohomology	2008	Richard Elman Nikita A. Karpenko Alexander Merkurjev
+ PDF Chat	The variety of maximal totally isotropic subspaces	2008	Richard Elman Nikita A. Karpenko Alexander Merkurjev
+	On the norm residue homomorphism of degree two	2008	Richard Elman Nikita A. Karpenko Alexander Merkurjev
+	Motives of quadrics	2008	Richard Elman Nikita A. Karpenko Alexander Merkurjev
+	Cycles on powers of quadrics	2008	Richard Elman Nikita A. Karpenko Alexander Merkurjev
+	Application of Steenrod operations	2008	Richard Elman Nikita A. Karpenko Alexander Merkurjev
+	Steenrod operations	2008	Richard Elman Nikita A. Karpenko Alexander Merkurjev
+	Quadratic forms	2008	Richard Elman Nikita A. Karpenko Alexander Merkurjev
+	The Algebraic and Geometric Theory of Quadratic Forms	2008	Richard Elman Nikita A. Karpenko Alexander Merkurjev
+	Unramified elements in cycle modules	2008	Alexander Merkurjev
+ PDF Chat	<i>R</i>-equivalence on three-dimensional tori and zero-cycles	2008	Alexander Merkurjev
+ PDF Chat	Essential dimension of finite p-groups	2008	Nikita A. Karpenko Alexander Merkurjev
+	Quadratic Forms and Linear Algebraic Groups	2007	Detlev W. Hoffmann Alexander Merkurjev Jean-Pierre Tignol
+	On the norm residue homomorphism of degree two	2006	Alexander Merkurjev
+ PDF Chat	Connectedness of classes of fields and zero-cycles on projective homogeneous varieties	2006	Vladimir Chernousov Alexander Merkurjev
+	Motivic decomposition of projective homogeneous varieties and the Krull-Schmidt theorem	2006	Vladimir Chernousov Alexander Merkurjev
+	The group SK1 for simple algebras	2006	Alexander Merkurjev
+	Rational surfaces and canonical dimension of PGL_6	2006	Jean-Louis Colliot-Thélène Nikita A. Karpenko Alexander Merkurjev
+	MOTIVIC DECOMPOSITION OF	2006	Projective Homogeneous Varieties Schmidt Theorem Vladimir Chernousov Alexander Merkurjev
+	Canonical<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>p</mml:mi></mml:math>-dimension of algebraic groups	2005	Nikita A. Karpenko Alexander Merkurjev
+	Motivic decomposition of isotropic projective homogeneous varieties	2005	Vladimir Chernousov Stefan Gille Alexander Merkurjev
+	Equivariant K-Theory	2005	Alexander Merkurjev
+	Appendix: My Recollections About Oleg Izhboldin	2004	Alexander Merkurjev
+ PDF Chat	Cohomological Invariants in Galois Cohomology	2003	Skip Garibaldi Alexander Merkurjev Jean Pierre Serre
+	The trace form in dimension \le7	2003	Skip Garibaldi Alexander Merkurjev Jean-Pierre Serre
+	Rost invariants of simply connected algebraic groups	2003	Skip Garibaldi Alexander Merkurjev Jean-Pierre Serre
+	Specialization properties of cohomological invariants	2003	Skip Garibaldi Alexander Merkurjev Jean-Pierre Serre
+	Cohomological preliminaries: The local case	2003	Skip Garibaldi Alexander Merkurjev Jean-Pierre Serre
+	Cohomological invariants of étale algebras	2003	Skip Garibaldi Alexander Merkurjev Jean-Pierre Serre
+	Cohomological preliminaries: The function field case	2003	Skip Garibaldi Alexander Merkurjev Jean-Pierre Serre
+	The groups 𝐻^{𝑑+1}(𝐹,ℚ/ℤ(𝕕))	2003	Skip Garibaldi Alexander Merkurjev Jean-Pierre Serre
+	Cohomological invariants of O_{𝑛}, SO_{𝑛},…	2003	Skip Garibaldi Alexander Merkurjev Jean-Pierre Serre
+	Steenrod operations and degree formulas	2003	Alexander Merkurjev
+	Report on the BIRS workshop	2003	Richard Elman Alexander Merkurjev Jan Min Carl Riehm
+	Invariants of quasi-trivial tori and the Rost invariant	2003	Alexander Merkurjev R. Parimala Jean-Pierre Tignol
+ PDF Chat	Unramified cohomology of classifying varieties for classical simply connected groups1	2002	Alexander Merkurjev
+ PDF Chat	Rost projectors and Steenrod operations	2002	Nikita A. Karpenko Alexander Merkurjev
+ PDF Chat	Algebraic oriented cohomology theories	2002	Alexander Merkurjev
+	𝑅-equivalence in spinor groups	2001	Vladimir Chernousov Alexander Merkurjev
+	Cohomological Invariants of Simply Connected Groups of Rank 3	2000	Alexander Merkurjev
+	NORM PRINCIPLE FOR REDUCTIVE ALGEBRAIC GROUPS	2000	Pedro B. Barquero Alexander Merkurjev
+	Invariants of algebraic groups	1999	Alexander Merkurjev
+	Invariants of algebraic groups	1999	Alexander Merkurjev
+	R-Equivalence and Special Unitary Groups	1998	Vladimir Chernousov Alexander Merkurjev
+	The Book of Involutions	1998	Max-Albert Knus Alexander Merkurjev Markus Rost Jean-Pierre Tignol
+	Algebras of degree four	1998	Max-Albert Knus Alexander Merkurjev Markus Rost Jean-Pierre Tignol
+	Trialitarian central simple algebras	1998	Max-Albert Knus Alexander Merkurjev Markus Rost Jean-Pierre Tignol
+ PDF Chat	Algebras of degree three	1998	Max-Albert Knus Alexander Merkurjev Markus Rost Jean-Pierre Tignol
+	Involutions and Hermitian forms	1998	Max-Albert Knus Alexander Merkurjev Markus Rost Jean-Pierre Tignol
+	Cubic Jordan algebras	1998	Max-Albert Knus Alexander Merkurjev Markus Rost Jean-Pierre Tignol
+	Galois cohomology	1998	Max-Albert Knus Alexander Merkurjev Markus Rost Jean-Pierre Tignol
+	Algebraic groups	1998	Max-Albert Knus Alexander Merkurjev Markus Rost Jean-Pierre Tignol
+	Index Reduction Formulas for Twisted Flag Varieties, II	1998	Alexander Merkurjev Ivan Panin Adrian R. Wadsworth
+	K-Theory and Algebraic Groups	1998	Alexander Merkurjev
+	K-Theory of Algebraic Tori and Toric Varieties	1997	Alexander Merkurjev Ivan Panin
+ PDF Chat	R-equivalence and rationality problem for semisimple adjoint classical algebraic groups	1996	Alexander Merkurjev
+	Index reduction formulas for twisted flag varieties, I.	1996	Alexander Merkurjev Ivan Panin Adrian R. Wadsworth
+	Mathematics in St. Petersburg	1996	Andrey Andreevich Bolibrukh Alexander Merkurjev N. Yu. Netsvetaev
+	The chameleon groups of Richard J. Thompson : automorphisms and dynamics . Extensions centrales de groupes algébriques simplement connexes et cohomologie galoisienne . Computation of the metaplectic kernel . R-equivalence and rationality problem for semisimple adjoint classical algebraic groups	1996	Matthew G. Brin Alexander Merkurjev Pierre Deligne Gopal Prasad Andrei S. Rapinchuk
+	𝐾-theory of simple algebras	1995	Alexander Merkurjev
+	Algebraic K-Theory and Galois Cohomology	1994	Alexander Merkurjev
+	Certain 𝐾-cohomology groups of Severi-Brauer varieties	1994	Alexander Merkurjev
+	Growth of the 𝑢-invariant under algebraic extensions	1994	David B. Leep Alexander Merkurjev
+	Galois cohomology of biquadratic extensions	1993	Alexander Merkurjev Jean-Pierre Tignol
+	On the corestriction ofp n -symbol	1991	P. Mammone Alexander Merkurjev
+	𝐾₂ of fields and the Brauer group	1986	Alexander Merkurjev
+	On the Torsion in K 2 of Local Fields	1983	Alexander Merkurjev
+	Brauer groups of fields	1983	Alexander Merkurjev

Common Coauthors

Coauthor	Papers Together
Nikita A. Karpenko	28
Jean-Pierre Tignol	16
Richard Elman	12
Vladimir Chernousov	12
Skip Garibaldi	10
Markus Rost	8
Max-Albert Knus	8
Jean-Pierre Serre	8
Federico Scavia	7
Vladyslav Yaskin	3
Ivan Panin	3
Olivier Haution	3
Nivedita Bhaskhar	3
Alexander Koldobsky	3
Detlev W. Hoffmann	3
Matthew Gherman	2
Boris M. Bekker	2
Sam Blinstein	2
Alexander Vishik	2
Adrian R. Wadsworth	2
О. А. Иванов	2
Sanghoon Baek	2
Jean Pierre Serre	1
Pascal Mammone	1
Gopal Prasad	1
Andrey Andreevich Bolibrukh	1
Schmidt Theorem	1
Carl Riehm	1
Matthew G. Brin	1
Andrei Suslin	1
Alexander Neshitov	1
Eric M. Friedlander	1
Stefan Gille	1
Donald Joseph Laackman	1
Kirill Zainoulline	1
Andrei S. Rapinchuk	1
Rostislav Devyatov	1
Projective Homogeneous Varieties	1
Jean-Louis Colliot-Thélène	1
Alexander Wertheim	1
Jan Min	1
Pierre Deligne	1
Zinovy Reichstein	1
Pedro B. Barquero	1
R. Parimala	1
N. Yu. Netsvetaev	1
David B. Leep	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	The Book of Involutions	1998	Max-Albert Knus Alexander Merkurjev Markus Rost Jean-Pierre Tignol	40
+ PDF Chat	Cohomological Invariants in Galois Cohomology	2003	Skip Garibaldi Alexander Merkurjev Jean Pierre Serre	32
+	Higher algebraic K-theory: I	1973	Daniel Quillen	24
+ PDF Chat	Chow groups with coefficients	1996	Markus Rost	21
+	$ K$-COHOMOLOGY OF SEVERI-BRAUER VARIETIES AND THE NORM RESIDUE HOMOMORPHISM	1983	A S Merkur'ev Andrei Suslin	19
+	The Algebraic and Geometric Theory of Quadratic Forms	2008	Richard Elman Nikita A. Karpenko Alexander Merkurjev	18
+ PDF Chat	La $R$-équivalence sur les tores	1977	Jean-Louis Colliot-Thélène Jean-Jacques Sansuc	14
+ PDF Chat	The Chow Ring of a Classifying Space	2014	Burt Totaro	12
+ PDF Chat	Cohomological invariants of algebraic tori	2013	Sam Blinstein Alexander Merkurjev	12
+ PDF Chat	Applications of weight-two motivic cohomology	1996	Bruno Kahn	12
+	The algebraic theory of quadratic forms	1973	T. Y. Lam	11
+	The multipliers of similitudes and the Brauer group of homogeneous varieties.	1995	Alexandr S. Merkurjev Jean-Pierre Tignol	11
+	Equivariant intersection theory	1998	Dan Edidin William Graham	11
+	Quadratic and Hermitian Forms	1985	Winfried Scharlau	10
+ PDF Chat	The Arason invariant and mod 2 algebraic cycles	1998	Hélène Esnault Bruno Kahn Marc Levine Eckart Viehweg	10
+	Représentations linéaires irréductibles d'un groupe réductif sur un corps quelconque.	1971	Jacques Tits	10
+ PDF Chat	Essential dimension: A functorial point of view (after A. Merkurjev)	2003	Grégory Berhuy Giordano Favi	10
+	AlgebraicK-theory and quadratic forms	1970	John Milnor	10
+	Motivic decomposition of isotropic projective homogeneous varieties	2005	Vladimir Chernousov Stefan Gille Alexander Merkurjev	10
+ PDF Chat	Essential Dimensions of Algebraic Groups and a Resolution Theorem for G-Varieties	2000	Zinovy Reichstein Boris Youssin	9
+	Cohomologische invarianten quadratischer Formen	1975	Jón Kr. Arason	9
+	Canonical<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>p</mml:mi></mml:math>-dimension of algebraic groups	2005	Nikita A. Karpenko Alexander Merkurjev	9
+ PDF Chat	Upper motives of algebraic groups and incompressibility of Severi–Brauer varieties	2012	Nikita A. Karpenko	8
+	Algebras with Involutions and the Classical Groups	1960	André Weil	8
+	On the algebraicK-theory of twisted flag varieties	1994	Ivan Panin	8
+	Invariants of algebraic groups	1999	Alexander Merkurjev	8
+	Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres.	1981	Jean-Jacques Sansuc	8
+	K-theory and K-cohomology of certain group varieties	1991	Andrei Suslin	8
+	Intersection Theory	1984	William Fulton	8
+	Index Reduction Formulas for Twisted Flag Varieties, II	1998	Alexander Merkurjev Ivan Panin Adrian R. Wadsworth	8
+	On the notion of essential dimension for algebraic groups	2000	Zinovy Reichstein	7
+	Linear algebraic groups	1966	Armand Borel	7
+ PDF Chat	On the notion of canonical dimension for algebraic groups	2005	Grégory Berhuy Zinovy Reichstein	7
+ PDF Chat	R-equivalence and rationality problem for semisimple adjoint classical algebraic groups	1996	Alexander Merkurjev	7
+ PDF Chat	Rationality properties of linear algebraic groups, II	1968	Armand Borel T. A. Springer	7
+	Algebraic Groups and Their Birational Invariants	2011	V E Voskresenskiĭ	7
+ PDF Chat	FIELDS OF DEFINITION FOR DIVISION ALGEBRAS	2003	Martin Lorenz Zinovy Reichstein Louis Rowen David J. Saltman	7
+	Function fields of generalized brauer-severi varieties	1991	Altha Blanchet	7
+	Algebraic K-theory and the norm-residue homomorphism	1985	Andrei Suslin	7
+	Formes quadratiques, groupes orthogonaux et alg�bres de Clifford	1968	Jacques Tits	7
+	Algèbres indécomposables d'exposant premier	1987	Jean-Pierre Tignol	7
+	Central Simple Algebras and Galois Cohomology	2006	Philippe Gille Tamás Szamuely	7
+	Cohomological invariants: exceptional groups and spin groups	2009	Skip Garibaldi	7
+ PDF Chat	Weight two motivic cohomology of classifying spaces for semisimple groups	2016	Alexander Merkurjev	6
+	The construction of weight-two arithmetic cohomology	1987	Stephen Lichtenbaum	6
+ PDF Chat	Degree three cohomological invariants of semisimple groups	2016	Alexander Merkurjev	6
+	A Variety Associated to an Algebra with Involution	1994	Daliao Tao	6
+ PDF Chat	The index of a Brauer class on a Brauer-Severi variety	1992	Aidan Schofield Michel Van den Bergh	6
+	Adams Operations and the Brown-Gersten-Quillen Spectral Sequence	2010	Alexander Merkurjev	6
+	Steenrod operations in Chow theory	2003	Patrick Brosnan	6