Bhargav Bhatt

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Bhargav Bhatt is a prominent mathematician specializing in algebraic geometry and arithmetic geometry, with significant contributions to p-adic Hodge theory. Born in India, he completed his undergraduate studies at the Massachusetts Institute of Technology (MIT) and earned his Ph.D. from Princeton University under the supervision of Aise Johan de Jong.


After his doctoral work, Bhatt joined the faculty at the University of Michigan, where he became a professor of mathematics. In 2020, he moved to the Institute for Advanced Study (IAS) in Princeton, New Jersey, where he continues his research and mentorship.


Bhatt's research focuses on areas such as:



  • Perfectoid Spaces: Building on the work of Peter Scholze, Bhatt has further developed the theory of perfectoid spaces, which has applications in number theory and algebraic geometry.

  • Prismatic Cohomology: He co-introduced prismatic cohomology, a new cohomological theory that unifies and extends various cohomology theories in arithmetic geometry.

  • Derived Algebraic Geometry: Bhatt has contributed to the advancement of derived algebraic geometry, incorporating homotopical methods into algebraic geometry.


His work has been recognized with several prestigious awards and honors:



  • 2015 Packard Fellowship for Science and Engineering: Awarded to innovative young scientists and engineers.

  • 2016 Blumenthal Award: Given by the American Mathematical Society (AMS) for significant contributions to the advancement of research in pure mathematics.

  • 2018 New Horizons in Mathematics Prize: Part of the Breakthrough Prizes, recognizing early-career achievements.

  • 2021 Frank Nelson Cole Prize in Algebra: Awarded by the AMS for outstanding contributions to algebra.

  • Invited Speaker at the International Congress of Mathematicians (ICM) 2018: A recognition of his significant contributions to mathematics.


As of my knowledge cutoff in October 2023, Bhargav Bhatt continues to be an influential figure in modern mathematics, contributing to cutting-edge research and mentoring emerging mathematicians in his field.

All published works
Action Title Year Authors
+ Arithmetic Geometry 2025 Bhargav Bhatt
Ana Caraiani
Герд Фалтингс
Peter Scholze
+ PDF Chat Perfectoid pure singularities 2024 Bhargav Bhatt
Linquan Ma
Zsolt Patakfalvi
Karl Schwede
Kevin Tucker
Joe Waldron
Jakub Witaszek
+ Test ideals in mixed characteristic: a unified theory up to perturbation 2024 Bhargav Bhatt
Linquan Ma
Zsolt Patakfalvi
Karl Schwede
Kevin Tucker
Joe Waldron
Jakub Witaszek
+ PDF Chat Frobenius on the Cohomology of Thickenings 2023 Bhargav Bhatt
Manuel Blickle
Gennady Lyubeznik
Anurag K. Singh
Wenliang Zhang
+ Algebraic geometry in mixed characteristic 2023 Bhargav Bhatt
+ PDF Chat Globally $\pmb{+}$-regular varieties and the minimal model program for threefolds in mixed characteristic 2023 Bhargav Bhatt
Linquan Ma
Zsolt Patakfalvi
Karl Schwede
Kevin Tucker
Joe Waldron
Jakub Witaszek
+ PDF Chat Prismatic $F$-crystals and crystalline Galois representations 2023 Bhargav Bhatt
Peter Scholze
+ PDF Chat Syntomic complexes and <i>p</i>-adic étale Tate twists 2023 Bhargav Bhatt
Akhil Mathew
+ Frobenius on the cohomology of thickenings 2023 Bhargav Bhatt
Manuel Blickle
Gennady Lyubeznik
Anurag K. Singh
Wenliang Zhang
+ Applications of perverse sheaves in commutative algebra 2023 Bhargav Bhatt
Manuel Blickle
Gennady Lyubeznik
Anurag K. Singh
Wenliang Zhang
+ Crystals and Chern classes 2023 Bhargav Bhatt
+ PDF Chat Prisms and prismatic cohomology 2022 Bhargav Bhatt
Peter Scholze
+ Automated repair of resource leaks in Android applications 2022 Bhargav Bhatt
Carlo A. Furia
+ PDF Chat The six functors for Zariski-constructible sheaves in rigid geometry 2022 Bhargav Bhatt
David J. Hansen
+ Syntomic complexes and $p$-adic étale Tate twists 2022 Bhargav Bhatt
Akhil Mathew
+ Absolute prismatic cohomology 2022 Bhargav Bhatt
Jacob Lurie
+ The prismatization of $p$-adic formal schemes 2022 Bhargav Bhatt
Jacob Lurie
+ The arc-topology 2021 Bhargav Bhatt
Akhil Mathew
+ PDF Chat An asymptotic vanishing theorem for the cohomology of thickenings 2021 Bhargav Bhatt
Manuel Blickle
Gennady Lyubeznik
Anurag K. Singh
Wenliang Zhang
+ PDF Chat Revisiting the de Rham-Witt complex 2021 Bhargav Bhatt
Jacob Lurie
Akhil Mathew
+ PDF Chat Counterexamples to Hochschild-Kostant-Rosenberg in characteristic <i>p</i> 2021 Benjamin Antieau
Bhargav Bhatt
Akhil Mathew
+ Totaro's inequality for classifying spaces 2021 Bhargav Bhatt
Shizhang Li
+ Algebraic geometry in mixed characteristic 2021 Bhargav Bhatt
+ The six functors for Zariski-constructible sheaves in rigid geometry 2021 Bhargav Bhatt
David Hansen
+ Prismatic $F$-crystals and crystalline Galois representations 2021 Bhargav Bhatt
Peter Scholze
+ Globally +-regular varieties and the minimal model program for threefolds in mixed characteristic 2020 Bhargav Bhatt
Linquan Ma
Zsolt Patakfalvi
Karl Schwede
Kevin Tucker
Joe Waldron
Jakub Witaszek
+ PDF Chat Remarks on K(1)-local K-theory 2020 Bhargav Bhatt
Dustin Clausen
Akhil Mathew
+ Remarks on $K(1)$-local $K$-theory 2020 Bhargav Bhatt
Dustin Clausen
Akhil Mathew
+ An asymptotic vanishing theorem for the cohomology of thickenings 2020 Bhargav Bhatt
Manuel Blickle
Gennady Lyubeznik
Anurag K. Singh
Wenliang Zhang
+ Cohen-Macaulayness of absolute integral closures 2020 Bhargav Bhatt
+ Globally +-regular varieties and the minimal model program for threefolds in mixed characteristic 2020 Bhargav Bhatt
Linquan Ma
Zsolt Patakfalvi
Karl Schwede
Kevin Tucker
Joe Waldron
Jakub Witaszek
+ Automated Repair of Resource Leaks in Android Applications 2020 Bhargav Bhatt
Carlo A. Furia
+ Remarks on $K(1)$-local $K$-theory 2020 Bhargav Bhatt
Dustin Clausen
Akhil Mathew
+ Perfectoid Shimura varieties 2019 Bhargav Bhatt
Ana Caraiani
Kiran S. Kedlaya
Peter Scholze
Jared Weinstein
+ Adic spaces 2019 Bhargav Bhatt
Ana Caraiani
Kiran S. Kedlaya
Peter Scholze
Jared Weinstein
+ Counterexamples to Hochschild--Kostant--Rosenberg in characteristic $p$ 2019 Benjamin Antieau
Bhargav Bhatt
Akhil Mathew
+ Topological Hochschild homology and integral p $p$ -adic Hodge theory 2019 Bhargav Bhatt
Matthew Morrow
Peter Scholze
+ PDF Chat Regular rings and perfect(oid) algebras 2019 Bhargav Bhatt
Srikanth B. Iyengar
Linquan Ma
+ PDF Chat A Riemann–Hilbert correspondence in positive characteristic 2019 Bhargav Bhatt
Jacob Lurie
+ PDF Chat Stabilization of the cohomology of thickenings 2019 Bhargav Bhatt
Manuel Blickle
Gennady Lyubeznik
Anurag K. Singh
Wenliang Zhang
+ Foliations with positive slopes and birational stability of orbifold cotangent bundles . Fourier interpolation on the real line . Joinings of higher rank torus actions on homogeneous spaces . Categorical actions on unipotent representations of finite unitary groups . Topological Hochschild homology and integral ρ-adic Hodge theory 2019 Frédéric Campana
Mihai Păun
Danylo Radchenko
Maryna Viazovska
Manfred Einsiedler
Elon Lindenstrauss
Olivier Dudas
Michela Varagnolo
Éric Vasserot
Bhargav Bhatt
+ Counterexamples to Hochschild--Kostant--Rosenberg in characteristic $p$ 2019 Benjamin Antieau
Bhargav Bhatt
Akhil Mathew
+ Prisms and Prismatic Cohomology 2019 Bhargav Bhatt
Peter Scholze
+ PDF Chat The pro-étale topology for schemes 2018 Bhargav Bhatt
Peter Scholze
+ Integral p $p$ -adic Hodge theory 2018 Bhargav Bhatt
Matthew Morrow
Peter Scholze
+ PDF Chat The weak ordinarity conjecture and $F$-singularities 2018 Bhargav Bhatt
Karl Schwede
Shunsuke Takagi
+ PDF Chat Torsion completions are bounded 2018 Bhargav Bhatt
+ Excision and arc-descent in \'etale cohomology 2018 Bhargav Bhatt
Akhil Mathew
+ The arc-topology 2018 Bhargav Bhatt
Akhil Mathew
+ PDF Chat Specializing varieties and their cohomology from characteristic 0 to characteristic 𝑝 2018 Bhargav Bhatt
+ PDF Chat Specializing varieties and their cohomology from characteristic 0 to characteristic 𝑝 2018 Bhargav Bhatt
+ Topological Hochschild homology and integral $p$-adic Hodge theory 2018 Bhargav Bhatt
Matthew Morrow
Peter Scholze
+ Regular rings and perfect(oid) algebras 2018 Bhargav Bhatt
Srikanth B. Iyengar
Linquan Ma
+ Measure concentration and the weak Pinsker property . Integral models of Shimura varieties with parahoric level structure . Integral p-adic Hodge theory 2018 Tim Austin
Mark Kisin
G. Pappas
Bhargav Bhatt
Matthew Morrow
Peter Scholze
+ Revisiting the de Rham-Witt complex 2018 Bhargav Bhatt
Jacob Lurie
Akhil Mathew
+ The arc-topology 2018 Bhargav Bhatt
Akhil Mathew
+ PDF Chat Vanishing theorems for perverse sheaves on abelian varieties, revisited 2017 Bhargav Bhatt
Christian Schnell
Peter Scholze
+ PDF Chat On the direct summand conjecture and its derived variant 2017 Bhargav Bhatt
+ A Riemann-Hilbert correspondence in positive characteristic 2017 Bhargav Bhatt
Jacob Lurie
+ PDF Chat The dualizing complex of F-injective and Du Bois singularities 2017 Bhargav Bhatt
Linquan Ma
Karl Schwede
+ PDF Chat Étale Fundamental Groups of Strongly $\boldsymbol{F}$-Regular Schemes 2017 Bhargav Bhatt
Javier Carvajal‐Rojas
Patrick Graf
Karl Schwede
Kevin Tucker
+ Tannaka duality revisited 2017 Bhargav Bhatt
Daniel Halpern-Leistner
+ Vanishing theorems for perverse sheaves on abelian varieties, revisited 2017 Bhargav Bhatt
Christian Schnell
Peter Scholze
+ Finiteness of étale fundamental groups by reduction modulo $p$ 2017 Bhargav Bhatt
Ofer Gabber
Martin Olsson
+ A Riemann-Hilbert correspondence in positive characteristic 2017 Bhargav Bhatt
Jacob Lurie
+ Vanishing theorems for perverse sheaves on abelian varieties, revisited 2017 Bhargav Bhatt
Christian Schnell
Peter Scholze
+ PDF Chat Projectivity of the Witt vector affine Grassmannian 2016 Bhargav Bhatt
Peter Scholze
+ On the direct summand conjecture and its derived variant 2016 Bhargav Bhatt
+ Integral p-adic Hodge theory 2016 Bhargav Bhatt
Matthew Morrow
Peter Scholze
+ Stabilization of the cohomology of thickenings 2016 Bhargav Bhatt
Manuel Blickle
Gennady Lyubeznik
Anurag K. Singh
Wenliang Zhang
+ PDF Chat Algebraization and Tannaka duality 2016 Bhargav Bhatt
+ Integral p-adic Hodge theory 2016 Bhargav Bhatt
Matthew Morrow
Peter Scholze
+ On the direct summand conjecture and its derived variant 2016 Bhargav Bhatt
+ Specializing varieties and their cohomology from characteristic $0$ to characteristic $p$ 2016 Bhargav Bhatt
+ PDF Chat -DIVISIBILITY FOR COHERENT COHOMOLOGY 2015 Bhargav Bhatt
+ Integral $p$-adic Hodge theory - announcement 2015 Bhargav Bhatt
Matthew Morrow
Peter Scholze
+ Projectivity of the Witt vector affine Grassmannian 2015 Bhargav Bhatt
Peter Scholze
+ Tannaka duality revisited 2015 Bhargav Bhatt
Daniel Halpern-Leistner
+ The Pro-étale topology for schemes 2015 Bhargav Bhatt
Peter Scholze
+ Projectivity of the Witt vector affine Grassmannian 2015 Bhargav Bhatt
Peter Scholze
+ Integral $p$-adic Hodge theory - announcement 2015 Bhargav Bhatt
Matthew Morrow
Peter Scholze
+ Tannaka duality revisited 2015 Bhargav Bhatt
Daniel Halpern-Leistner
+ The $$F$$ F -pure threshold of a Calabi–Yau hypersurface 2014 Bhargav Bhatt
Anurag K. Singh
+ PDF Chat Almost direct summands 2014 Bhargav Bhatt
+ On the non-existence of small Cohen–Macaulay algebras 2014 Bhargav Bhatt
+ Algebraization and Tannaka duality 2014 Bhargav Bhatt
+ PDF Chat Almost direct summands 2014 Bhargav Bhatt
+ PDF Chat Torsion in the crystalline cohomology of singular varieties 2014 Bhargav Bhatt
+ PDF Chat Lefschetz for Local Picard groups 2014 Bhargav Bhatt
A. J. de Jong
+ Algebraization and Tannaka duality 2014 Bhargav Bhatt
+ PDF Chat Local cohomology modules of a smooth $\mathbb{Z}$ -algebra have finitely many associated primes 2013 Bhargav Bhatt
Manuel Blickle
Gennady Lyubeznik
Anurag K. Singh
Wenliang Zhang
+ PDF Chat Moduli of products of stable varieties 2013 Bhargav Bhatt
Wei Ho
Zsolt Patakfalvi
Christian Schnell
+ The F-pure threshold of a Calabi-Yau hypersurface 2013 Bhargav Bhatt
Anurag K. Singh
+ Lefschetz for local Picard groups 2013 Bhargav Bhatt
A. J. de Jong
+ The weak ordinarity conjecture and $F$-singularities 2013 Bhargav Bhatt
Karl Schwede
Shunsuke Takagi
+ Lefschetz for local Picard groups 2013 Bhargav Bhatt
A. J. de Jong
+ The F-pure threshold of a Calabi-Yau hypersurface 2013 Bhargav Bhatt
Anurag K. Singh
+ The pro-étale topology for schemes 2013 Bhargav Bhatt
Peter Scholze
+ PDF Chat Annihilating the cohomology of group schemes 2012 Bhargav Bhatt
+ PDF Chat Log canonical thresholds,<i>F</i>-pure thresholds, and nonstandard extensions 2012 Bhargav Bhatt
Daniel J. Hernández
Lance Edward Miller
Mircea Mustaţǎ
+ PDF Chat Derived splinters in positive characteristic 2012 Bhargav Bhatt
+ Torsion in the crystalline cohomology of singular varieties 2012 Bhargav Bhatt
+ A note on the non-existence of small Cohen-Macaulay algebras 2012 Bhargav Bhatt
+ p-adic derived de Rham cohomology 2012 Bhargav Bhatt
+ Completions and derived de Rham cohomology 2012 Bhargav Bhatt
+ p-divisibility for coherent cohomology 2012 Bhargav Bhatt
+ Algebra & Number Theory 2012 Bhargav Bhatt
Daniel J. Hernández
Lance Edward Miller
Mircea Mustat
+ Torsion in the crystalline cohomology of singular varieties 2012 Bhargav Bhatt
+ Annihilating the cohomology of group schemes 2011 Bhargav Bhatt
+ Log canonical thresholds, F-pure thresholds, and non-standard extensions 2011 Bhargav Bhatt
Daniel J. Hernández
Lance Edward Miller
Mircea Mustaţǎ
+ Crystalline cohomology and de Rham cohomology 2011 Bhargav Bhatt
A. J. de Jong
+ Log canonical thresholds, F-pure thresholds, and non-standard extensions 2011 Bhargav Bhatt
Daniel J. Hernández
Lance Edward Miller
Mircea Mustaţǎ
+ Annihilating the cohomology of group schemes 2011 Bhargav Bhatt
+ DERIVED DIRECT SUMMANDS 2010 Bhargav Bhatt
Common Coauthors
Commonly Cited References
Action Title Year Authors # of times referenced
+ Integral p $p$ -adic Hodge theory 2018 Bhargav Bhatt
Matthew Morrow
Peter Scholze
11
+ Almost Ring Theory 2003 Ofer Gabber
Lorenzo Ramero
10
+ PDF Chat Smoothness, semi-stability and alterations 1996 A. J. de Jong
10
+ Rel�vements modulop 2 et d�composition du complexe de de Rham 1987 Pierre Deligne
Luc Illusie
10
+ Infinite Integral Extensions and big Cohen--Macaulay Algebras 1992 Melvin Hochster
Craig Huneke
9
+ Absolute integral closure in positive characteristic 2006 Craig Huneke
Gennady Lyubeznik
9
+ PDF Chat Projectivity of the Witt vector affine Grassmannian 2016 Bhargav Bhatt
Peter Scholze
8
+ PDF Chat Homological conjectures, old and new 2007 Melvin Hochster
8
+ A generalization of tight closure and multiplier ideals 2003 Nobuo Hara
Ken Yoshida
8
+ PDF Chat On topological cyclic homology 2018 Thomas Nikolaus
Peter Scholze
8
+ PDF Chat Derived splinters in positive characteristic 2012 Bhargav Bhatt
7
+ PDF Chat Locally Complete Intersection Homomorphisms and a Conjecture of Quillen on the Vanishing of Cotangent Homology 1999 Luchézar L. Avramov
7
+ PDF Chat -ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES 2013 Peter Scholze
7
+ PDF Chat 𝑝-adic Hodge theory 1988 Герд Фалтингс
7
+ Notes on Crystalline Cohomology. 2015 Pierre Berthelot
Arthur Ogus
7
+ Éléments de géométrie algébrique 1964 Alexandre Grothendieck
7
+ The Pro-étale topology for schemes 2015 Bhargav Bhatt
Peter Scholze
7
+ Higher Topos Theory 2009 Jacob Lurie
7
+ PDF Chat A characterization of rational singularities in terms of injectivity of Frobenius maps 1998 Nobuo Hara
7
+ F-rational rings have rational singularities 1997 Karen E. Smith
7
+ p-adic étale cohomology and crystalline cohomology in the semi-stable reduction case 1999 Takeshi Tsuji
7
+ Éléments de Géométrie algébrique 1960 Alexandre Grothendieck
Jean Dieudonné
6
+ PDF Chat Discreteness and rationality of F-jumping numbers on singular varieties 2009 Manuel Blickle
Karl Schwede
Shunsuke Takagi
Wenliang Zhang
6
+ Perfectoid Spaces 2012 Peter Scholze
6
+ PDF Chat The Direct Summand Conjecture in Dimension Three 2002 Raymond C. Heitmann
6
+ PDF Chat A characterization of rational singularities 1997 V. B. Mehta
V. Srinivas
6
+ F-regular and F-pure rings vs. log terminal and log canonical singularities 2001 Nobuo Hara
Kei-ichi Watanabe
6
+ Étale Cohomology of Rigid Analytic Varieties and Adic Spaces 1996 Roland Huber
6
+ PDF Chat Singular homology of abstract algebraic varieties 1996 Andrei Suslin
Vladimir Voevodsky
6
+ PDF Chat Contracted ideals from integral extensions of regular rings 1973 Melvin Hochster
6
+ PDF Chat Complexe de de\thinspace Rham-Witt et cohomologie cristalline 1979 Luc Illusie
6
+ PDF Chat An interpretation of multiplier ideals via tight closure 2004 Shunsuke Takagi
5
+ p-adic derived de Rham cohomology 2012 Bhargav Bhatt
5
+ Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux 1962 Alexandre Grothendieck
5
+ PDF Chat Integral crystalline cohomology over very ramified valuation rings 1999 Герд Фалтингс
5
+ PDF Chat Syntomic complexes and p-adic nearby cycles 2016 Pierre Colmez
Wiesława Nizioł
5
+ Higher Algebraic K-Theory of Schemes and of Derived Categories 2007 R. W. Thomason
Thomas Trobaugh
5
+ PDF Chat $p$-adic periods and derived de Rham cohomology 2012 Alexander Beilinson
5
+ Local Cohomological Dimension in Characteristic p 1977 Robin Hartshorne
Robert Speiser
5
+ PDF Chat On the direct summand conjecture and its derived variant 2017 Bhargav Bhatt
5
+ PDF Chat Complexe Cotangent et Déformations I 1971 Luc Illusie
5
+ Frobenius Splitting and Cohomology Vanishing for Schubert Varieties 1985 V. B. Mehta
A. Ramanathan
5
+ PDF Chat La conjecture du facteur direct 2017 Yves André
5
+ PDF Chat Les suites spectrales associées au complexe de de Rham-Witt 1983 Luc Illusie
Michel Raynaud
5
+ PDF Chat The de Rham-Witt complex and 𝑝-adic vanishing cycles 2005 Thomas Geisser
Lars Hesselholt
5
+ Almost étale extensions 2002 Герд Фалтингс
5
+ F-thresholds and Bernstein-Sato polynomials 2004 Mircea Mustaţǎ
Shunsuke Takagi
Kei-ichi Watanabe
5
+ Sur Certains Types de Representations p-Adiques du Groupe de Galois d'un Corps Local; Construction d'un Anneau de Barsotti-Tate 1982 Jean-Marc Fontaine
5
+ The Galois group of a stable homotopy theory 2016 Akhil Mathew
5
+ PDF Chat Basepoint Freeness for Nef and Big Line Bundles in Positive Characteristic 1999 Seán Keel
4