Andrei S. Rapinchuk

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All published works
Action Title Year Authors
+ The finiteness of the Tate–Shafarevich group over function fields for algebraic tori defined over the base field 2024 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ PDF Chat Simple algebraic groups with the same maximal tori, weakly commensurable Zariski-dense subgroups, and good reduction 2023 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ Algebraic Number Theory 2023 В. П. Платонов
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ Algebraic Groups and Number Theory 2023 В. П. Платонов
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ PDF Chat Applications of the Fixed Point Theorem for group actions on buildings to algebraic groups over polynomial rings 2023 Peter Abramenko
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ PDF Properness of the global-to-local map for algebraic groups with toric connected component and other finiteness properties 2023 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ The finiteness of the Tate-Shafarevich group over function fields for algebraic tori defined over the base field 2023 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ Purely exponential parametrizations and their group-theoretic applications 2023 Pietro Corvaja
Julian Lawrence Demeio
Andrei S. Rapinchuk
Jinbo Ren
Umberto Zannier
+ PDF Bounded Generation by semi-simple elements: quantitative results 2022 Pietro Corvaja
Julian Lawrence Demeio
Andrei S. Rapinchuk
Jinbo Ren
Umberto Zannier
+ Bounded Generation by semi-simple elements: quantitative results 2022 Pietro Corvaja
Julian Lawrence Demeio
Andrei S. Rapinchuk
Jinbo Ren
Umberto Zannier
+ Applications of the Fixed Point Theorem for group actions on buildings to algebraic groups over polynomial rings 2022 Peter Abramenko
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ PDF Chat Simple algebraic groups with the same maximal tori, weakly commensurable Zariski-dense subgroups, and good reduction 2021 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ PDF Finiteness theorems for algebraic tori over function fields 2021 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ PDF Chat Non-virtually abelian anisotropic linear groups are not boundedly generated 2021 Pietro Corvaja
Andrei S. Rapinchuk
Jinbo Ren
Umberto Zannier
+ PDF Chat Some finiteness results for algebraic groups and unramified cohomology over higher-dimensional fields 2021 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ Division algebras with common subfields 2021 Daniel Krashen
Eliyahu Matzri
Andrei S. Rapinchuk
Louis Rowen
David J. Saltman
+ Recent Developments in the Theory of Linear Algebraic Groups: Good Reduction and Finiteness Properties 2021 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ Recent developments in the theory of linear algebraic groups: Good reduction and finiteness properties 2021 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ Non-virtually abelian anisotropic linear groups are not boundedly generated 2021 Pietro Corvaja
Andrei S. Rapinchuk
Jinbo Ren
Umberto Zannier
+ Simple algebraic groups with the same maximal tori, weakly commensurable Zariski-dense subgroups, and good reduction 2021 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ Recent developments in the theory of linear algebraic groups: Good reduction and finiteness properties 2021 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ Properness of the global-to-local map for algebraic groups with toric connected component and other finiteness properties 2021 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ PDF Chat Linear algebraic groups with good reduction 2020 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ Linear algebraic groups with good reduction 2020 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ PDF Chat The finiteness of the genus of a finite-dimensional division algebra, and some generalizations 2020 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ Some finiteness results for algebraic groups and unramified cohomology over higher-dimensional fields 2020 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ Linear algebraic groups with good reduction 2020 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ Some finiteness results for algebraic groups and unramified cohomology over higher-dimensional fields 2020 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ PDF Chat Spinor groups with good reduction 2019 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ PDF Chat Bounded generation of SL2 over rings of S-integers with infinitely many units 2018 Aleksander Morgan
Andrei S. Rapinchuk
B. Sury
+ The finiteness of the genus of a finite-dimensional division algebra, and some generalizations 2018 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ The finiteness of the genus of a finite-dimensional division algebra, and some generalizations 2018 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ PDF Generic elements of a Zariski-dense subgroup form an open subset 2017 Gopal Prasad
Andrei S. Rapinchuk
+ Generic elements of a Zariski-dense subgroup form an open subset 2017 Gopal Prasad
Andrei S. Rapinchuk
+ Generic elements of a Zariski-dense subgroup form an open subset 2017 Gopal Prasad
Andrei S. Rapinchuk
+ On some finiteness properties of algebraic groups over finitely generated fields 2016 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ PDF Chat On the Size of the Genus of a Division Algebra 2016 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ PDF Chat On the congruence kernel for simple algebraic groups 2016 Gopal Prasad
Andrei S. Rapinchuk
+ PDF Chat On the Congruence Kernel for Simple Algebraic Groups 2016 Gopal Prasad
Andrei S. Rapinchuk
+ PDF Chat On the size of the genus of a division algebra 2016 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ PDF Chat Division algebras with the same maximal subfields 2015 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ Vladimir Petrovich Platonov (on his 75th birthday) 2015 Сергей Иванович Адян
Valerii Vatslavovich Benyash-Krivets
Victor Matveevich Buchstaber
Efim Zelmanov
Валерий Васильевич Козлов
Григорий Александрович Маргулис
S P Novikov
Алексей Николаевич Паршин
Гопал Прасад
Andrei S. Rapinchuk
+ PDF Vladimir Petrovich Platonov (on his 75th birthday) 2015 Сергей Иванович Адян
Valerii Vatslavovich Benyash-Krivets
Victor Matveevich Buchstaber
Efim Zelmanov
Valery Vasil'evich Kozlov
Григорий Александрович Маргулис
Сергей Петрович Новиков
Alexey Nikolaevich Parshin
Гопал Прасад
Andrei S. Rapinchuk
+ PDF Division algebras with the same maximal subfields 2015 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ On the size of the genus of a division algebra 2015 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ On the congruence kernel for simple algebraic groups 2015 Gopal Prasad
Andrei S. Rapinchuk
+ On graphs and valuations 2014 Ido Efrat
Andrei S. Rapinchuk
Yoav Segev
+ On graphs and valuations 2014 Ido Efrat
Andrei S. Rapinchuk
Yoav Segev
+ On graphs and valuations 2014 Ido Efrat
Andrei S. Rapinchuk
Yoav Segev
+ PDF Chat On the fields generated by the lengths of closed geodesics in locally symmetric spaces 2013 Gopal Prasad
Andrei S. Rapinchuk
+ PDF Weakly commensurable<i>S</i>-arithmetic subgroups in almost simple algebraic groups of types B and C 2013 Skip Garibaldi
Andrei S. Rapinchuk
+ PDF The genus of a division algebra and the unramified Brauer group 2013 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ On the congruence subgroup problem 2013 Andrei S. Rapinchuk
+ The genus of a division algebra and the unramified Brauer group 2013 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ Weakly commensurable groups, with applications to differential geometry 2013 Gopal Prasad
Andrei S. Rapinchuk
+ Arithmetic Groups (Banff, Alberta, April 14-19, 2013) 2013 Kai‐Uwe Bux
Dave Witte Morris
Gopal Prasad
Andrei S. Rapinchuk
+ The genus of a division algebra and the unramified Brauer group 2013 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ The multinorm principle for linearly disjoint Galois extensions 2012 Timothy P. Pollio
Andrei S. Rapinchuk
+ On the genus of a division algebra 2012 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
+ On strong approximation for algebraic groups 2012 Andrei S. Rapinchuk
+ The Multinorm Principle For Linearly Disjoint Galois Extensions 2012 Timothy P. Pollio
Andrei S. Rapinchuk
+ Generic elements in Zariski-dense subgroups and isospectral locally symmetric spaces 2012 Gopal Prasad
Andrei S. Rapinchuk
+ On strong approximation for algebraic groups 2012 Andrei S. Rapinchuk
+ The Multinorm Principle For Linearly Disjoint Galois Extensions 2012 Timothy P. Pollio
Andrei S. Rapinchuk
+ On the fields generated by the lengths of closed geodesics in locally symmetric spaces 2011 Gopal Prasad
Andrei S. Rapinchuk
+ PDF The congruence subgroup property for Aut $F_2$: A group-theoretic proof of Asada’s theorem 2011 Kai‐Uwe Bux
Mikhail Ershov
Andrei S. Rapinchuk
+ Centrality of the congruence kernel for elementary subgroups of Chevalley groups of rank &gt;1 over noetherian rings 2011 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ On the fields generated by the lengths of closed geodesics in locally symmetric spaces 2011 Gopal Prasad
Andrei S. Rapinchuk
+ Centrality of the congruence kernel for elementary subgroups of Chevalley groups of rank >1 over noetherian rings 2010 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ PDF Local–global principles for embedding of fields with involution into simple algebras with involution 2010 Gopal Prasad
Andrei S. Rapinchuk
+ PDF Chat On division algebras having the same maximal subfields 2010 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ Centrality of the congruence kernel for elementary subgroups of Chevalley groups of rank &gt;1 over noetherian rings 2010 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ PDF Chat Weakly commensurable arithmetic groups and isospectral locally symmetric spaces 2009 Gopal Prasad
Andrei S. Rapinchuk
+ On division algebras having the same maximal subfields 2009 Andrei S. Rapinchuk
Igor A. Rapinchuk
+ Three results on the regularity of the curves that are invariant by an exact symplectic twist map . Invariant subspaces for operators in a general II[1]-factor . Weakly commensurable arithmetic groups and isospectral locally symmetric spaces . The C[1] generic diffeomorphism has trivial centralizer . Finitude homotopique et isotopique des structures de contact tendues . Deux caractérisations de la mesure d'équilibre d'un endomorphisme de P[k](C) (Erratum) 2009 Marie-Claude Arnaud
Uffe Haagerup
Hanne Schultz
Gopal Prasad
Andrei S. Rapinchuk
Christian Bonatti
Sylvain Crovisier
Amie Wilkinson
Vincent Colin
Emmanuel Giroux
+ Number theoretic techniques in the theory of Lie groups and differential geometry 2008 Gopal Prasad
Andrei S. Rapinchuk
+ Developments on the congruence subgroup problem after the work of Bass, Milnor and Serre 2008 Gopal Prasad
Andrei S. Rapinchuk
+ Local-global principles for embedding of fields with involution into simple algebras with involution 2008 Gopal Prasad
Andrei S. Rapinchuk
+ PDF Nonabelian free subgroups in homomorphic images of valued quaternion division algebras 2006 Andrei S. Rapinchuk
Louis Rowen
Yoav Segev
+ On the existence of isotropic forms of semi-simple algebraic groups over number fields with prescribed local behavior 2006 Gopal Prasad
Andrei S. Rapinchuk
+ Bounded generation of S-arithmetic subgroups of isotropic orthogonal groups over number fields 2006 Igor V. Erovenko
Andrei S. Rapinchuk
+ The Margulis-Platonov conjecture for SL1,D and 2-generation of finite simple groups 2005 Andrei S. Rapinchuk
+ PDF Zariski-dense subgroups and transcendental number theory 2005 Gopal Prasad
Andrei S. Rapinchuk
+ Bounded generation of S-arithmetic subgroups of isotropic orthogonal groups over number fields 2005 Igor V. Erovenko
Andrei S. Rapinchuk
+ Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable 2002 Andrei S. Rapinchuk
Yoav Segev
Gary M. Seitz
+ PDF Subnormal subgroups of the groups of rational points of reductive algebraic groups 2002 Gopal Prasad
Andrei S. Rapinchuk
+ None 2002 Gopal Prasad
Andrei S. Rapinchuk
+ Bounded generation of some -arithmetic orthogonal groups 2001 Igor V. Erovenko
Andrei S. Rapinchuk
+ On Abstract Homomorphisms of Chevalley Groups with Nonreductive Image, I 2001 Lucy Lifschitz
Andrei S. Rapinchuk
+ Valuation-like maps and the congruence subgroup property 2001 Andrei S. Rapinchuk
Yoav Segev
+ None 2001 Gopal Prasad
Andrei S. Rapinchuk
+ On the finite dimensional unitary representations of Kazhdan groups 1999 Andrei S. Rapinchuk
+ On SS -rigid groups and A. Weil's criterion for local rigidity. I 1998 Andrei S. Rapinchuk
+ On an approximation property for nondiscrete inequivalent representations of finitely generated groups 1998 Andrei S. Rapinchuk
+ n-Dimensional Linear Representations of AutFn, and More 1997 Andrei S. Rapinchuk
+ PDF Computation of the metaplectic kernel 1996 Gopal Prasad
Andrei S. Rapinchuk
+ PDF Representation varieties of the fundamental groups of compact orientable surfaces 1996 Andrei S. Rapinchuk
V. V. Benyash-Krivetz
Vladimir Chernousov
+ Normal subgroups ofSL 1,D and the classification of finite simple groups 1996 Andrei S. Rapinchuk
Alexander Potapchik
+ 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
+ G 1995 A. F. Kharshiladze
D. V. Alekseevskiĭ
N. N. Vorob’ëv
V. A. Trenogin
A. Z. Petrov
D. D. Sokolov
E. A. Nisnevich
A. I. Skopin
S. P. Demushkin
В. П. Платонов
+ R 1995 L. A. Skornyakov
I.P. Mysovskikh
A. A. Talalyan
E. D. Solomentsev
A. G. Sveshnikov
V. A. Chuyanov
A. L. Shmel’kin
V. A. Andrunakievich
R. A. Minlos
K. Yu. Bulota
+ ABSTRACT PROPERTIES OF $ S$-ARITHMETIC GROUPS AND THE CONGRUENCE PROBLEM 1993 В. П. Платонов
Andrei S. Rapinchuk
+ The geometric theory of representations for the fundamental groups of compact oriented surfaces 1993 Andrei S. Rapinchuk
Valerii Vatslavovich Benyash-Krivets
+ The metaplectic kernel for the group 𝑆𝐿(1,𝐷) 1992 Andrei S. Rapinchuk
+ PDF On the metaplectic kernel for anisotropic groups 1992 Andrei S. Rapinchuk
+ Algebraic groups and number theory 1992 В. П. Платонов
Andrei S. Rapinchuk
+ Structure of groups of rational points of classical algebraic groups over number fields 1990 В. П. Платонов
Andrei S. Rapinchuk
+ PDF The congruence subgroup problem for algebraic groups 1990 Andrei S. Rapinchuk
+ MULTIPLICATIVE ARITHMETIC OF DIVISION ALGEBRAS OVER NUMBER FIELDS, AND THE METAPLECTIC PROBLEM 1988 Andrei S. Rapinchuk
+ Thirteen Papers in Algebra and Number Theory 1986 I. Zhuk
I. Sh. Slavutskii
V. A. Lipnitskiĭ
Vladimir Chernousov
O. M. Adamovich
Yuriy Drozd
В. М. Бондаренко
A. G. Zavadskiĭ
Larisa Nazarova
Valentin F. Turchin
+ On Platonov’s conjecture on genus in arithmetic groups 1986 Andrei S. Rapinchuk
+ Algebraic groups 1985 В. П. Платонов
Andrei S. Rapinchuk
Common Coauthors
Commonly Cited References
Action Title Year Authors # of times referenced
+ Algebraic groups and number theory 1992 В. П. Платонов
Andrei S. Rapinchuk
49
+ PDF Chat Weakly commensurable arithmetic groups and isospectral locally symmetric spaces 2009 Gopal Prasad
Andrei S. Rapinchuk
23
+ Algebraic Groups and Number Theory 1994 20
+ Linear algebraic groups 1966 Armand Borel
17
+ PDF Existence of irreducible ${\mathbb R}$-regular elements in Zariski-dense subgroups 2003 Gopal Prasad
16
+ Algebraic Groups and Their Birational Invariants 2011 V E Voskresenskiĭ
15
+ Discrete Subgroups of Semisimple Lie Groups 1991 Gregori Aleksandrovitch Margulis
13
+ Isospectrality and commensurability of arithmetic hyperbolic 2- and 3-manifolds 1992 Alan W. Reid
12
+ None 2001 Gopal Prasad
Andrei S. Rapinchuk
12
+ Galois Cohomology 1997 Jean-Pierre Serre
12
+ PDF Computation of the metaplectic kernel 1996 Gopal Prasad
Andrei S. Rapinchuk
12
+ Generic elements in Zariski-dense subgroups and isospectral locally symmetric spaces 2012 Gopal Prasad
Andrei S. Rapinchuk
11
+ Solution of the congruence subgroup problem for SL n (n ≥ 3) and Sp2n (n ≥ 2) 1967 Hyman Bass
John Milnor
Jean-Pierre Serre
11
+ PDF Chat On division algebras having the same maximal subfields 2010 Andrei S. Rapinchuk
Igor A. Rapinchuk
11
+ PDF Chat Division algebras with infinite genus 2014 Jeffrey S. Meyer
11
+ Linear Algebraic Groups 1991 Armand Borel
10
+ Subgroup growth and congruence subgroups 1995 Alexander Lubotzky
10
+ Associative Algebras 1982 R. S. Pierce
10
+ PDF Chat Spinor groups with good reduction 2019 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
10
+ PDF Algebraic number theory 1999 Kazuya Katô
Nobushige Kurokawa
Takeshi Saito
10
+ Bounded Elementary Generation of SL n (O) 1983 David Carter
Gordon Keller
10
+ Fundamentals of Diophantine Geometry 1983 Serge Lang
10
+ Linear Algebraic Groups 1998 T. A. Springer
10
+ Lectures on Division Algebras 1999 David J. Saltman
10
+ Central Simple Algebras and Galois Cohomology 2006 Philippe Gille
Tamás Szamuely
10
+ Le Probleme des Groupes de Congruence Pour SL 2 1970 Jean-Pierre Serre
10
+ Lectures on Division Algebras 1999 David J. Saltman
9
+ On the genus of a division algebra 2012 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
9
+ PDF Sur le groupe des classes d’un schéma arithmétique 2006 Bruno Kahn
9
+ PDF The genus of a division algebra and the unramified Brauer group 2013 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
9
+ Strong Approximation for Semi-Simple Groups Over Function Fields 1977 Gopal Prasad
8
+ DISCRETE SUBGROUPS OF LIE GROUPS 1972 Raghunathan
8
+ RINGS OF DEFINITION OF DENSE SUBGROUPS OF SEMISIMPLE LINEAR GROUPS 1971 É. B. Vinberg
8
+ PDF Some finiteness properties of adele groups over number fields 1963 Armand Borel
8
+ Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable 2002 Andrei S. Rapinchuk
Yoav Segev
Gary M. Seitz
8
+ Groups over ℤ 1996 Benedict H. Gross
8
+ PDF Chat On the size of the genus of a division algebra 2016 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
8
+ PDF Multiplicative subgroups of finite index in a ring 1992 Vitaly Bergelson
Daniel B. Shapiro
8
+ PDF Chat On Finite Homomorphic Images of the Multiplicative Group of a Division Algebra 1999 Yoav Segev
8
+ PDF Chat Linear algebraic groups with good reduction 2020 Andrei S. Rapinchuk
Igor A. Rapinchuk
7
+ PDF Chat The finiteness of the genus of a finite-dimensional division algebra, and some generalizations 2020 Vladimir Chernousov
Andrei S. Rapinchuk
Igor A. Rapinchuk
7
+ Local Fields 1979 Jean-Pierre Serre
7
+ Valuation-like maps and the congruence subgroup property 2001 Andrei S. Rapinchuk
Yoav Segev
7
+ ABSTRACT PROPERTIES OF $ S$-ARITHMETIC GROUPS AND THE CONGRUENCE PROBLEM 1993 В. П. Платонов
Andrei S. Rapinchuk
7
+ PDF Division algebras of prime degree with infinite genus 2016 Sergey V. Tikhonov
7
+ Valuation theory on finite dimensional division algebras 2002 Adrian R. Wadsworth
7
+ Generic Splitting Fields of Central Simple Algebras 1955 S. A. Amitsur
7
+ PDF Chat On the fields generated by the lengths of closed geodesics in locally symmetric spaces 2013 Gopal Prasad
Andrei S. Rapinchuk
7
+ Groupes et algèbres de Lie 1971 Nicolás Bourbaki
7
+ Discrete Subgroups of Lie Groups 1972 M. S. Raghunathan
7