# Brian Conrad

#13,188

Most Influential Person Now

American mathematician

## Brian Conrad's AcademicInfluence.com Rankings

Brian Conradmathematics Degrees

Mathematics

#594

World Rank

#1114

Historical Rank

#265

USA Rank

Measure Theory

#3307

World Rank

#3908

Historical Rank

#956

USA Rank

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Mathematics

## Brian Conrad's Degrees

- Bachelors Mathematics Princeton University

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## Why Is Brian Conrad Influential?

(Suggest an Edit or Addition)According to Wikipedia, Brian Conrad is an American mathematician and number theorist, working at Stanford University. Previously, he taught at the University of Michigan and at Columbia University. Conrad and others proved the modularity theorem, also known as the Taniyama-Shimura Conjecture. He proved this in 1999 with Christophe Breuil, Fred Diamond and Richard Taylor, while holding a joint postdoctoral position at Harvard University and the Institute for Advanced Study in Princeton, New Jersey.

## Brian Conrad's Published Works

### Published Works

- On the modularity of elliptic curves over Q (2001) (628)
- On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises (2001) (325)
- Pseudo-reductive Groups (2010) (292)
- Grothendieck Duality and Base Change (2001) (267)
- Modularity of Certain Potentially Barsotti-Tate Galois Representations (1999) (190)
- Irreducible components of rigid spaces (1999) (181)
- Reductive Group Schemes (2014) (163)
- DELIGNE’S NOTES ON NAGATA COMPACTIFICATIONS (2009) (154)
- A MODERN PROOF OF CHEVALLEY’S THEOREM ON ALGEBRAIC GROUPS (2004) (131)
- Chow's K/k-image and K/k-trace, and the Lang-Neron theorem (2006) (126)
- ARITHMETIC MODULI OF GENERALIZED ELLIPTIC CURVES (2006) (107)
- Complex Multiplication and Lifting Problems (2013) (87)
- $J_1(p)$ has connected fibers (2003) (73)
- THE KEEL – MORI THEOREM VIA STACKS (2005) (68)
- Weil and Grothendieck approaches to adelic points (2012) (66)
- Relative ampleness in rigid geometry (2006) (66)
- Several approaches to non-archimedean geometry (2008) (63)
- Nagata compactification for algebraic spaces (2009) (56)
- Gross--Zagier Revisited (2004) (56)
- Finiteness theorems for algebraic groups over function fields (2011) (52)
- Arithmetic Algebraic Geometry (2008) (47)
- Non-archimedean analytification of algebraic spaces (2007) (44)
- LIFTING GLOBAL REPRESENTATIONS WITH LOCAL PROPERTIES (2011) (42)
- Power laws for monkeys typing randomly: the case of unequal probabilities (2004) (41)
- Approximation of versal deformations (2002) (39)
- Finite Group Schemes over Bases with Low Ramification (1999) (39)
- Root numbers and ranks in positive characteristic (2004) (31)
- Component Groups of Purely Toric Quotients (2001) (29)
- HIGHER-LEVEL CANONICAL SUBGROUPS IN ABELIAN VARIETIES (2006) (27)
- Modular Curves and Rigid-Analytic Spaces (2006) (25)
- Ramified deformation problems (1999) (23)
- Migration ofAntigen-Specific T Cells Away from CXCR4-Binding Human ImmunodeficiencyVirus Type 1gp120 (2004) (23)
- -adic Geometry: Lectures from the 2007 Arizona Winter School (2008) (22)
- An introduction to the conjecture of Bloch and Kato (2010) (20)
- P-adic L-functions and the coniveau filtration on Chow groups (2017) (18)
- Prime specialization in genus 0 (2008) (17)
- Classification of Pseudo-reductive Groups (2015) (16)
- MINIMAL MODELS FOR ELLIPTIC CURVES (2003) (16)
- The Flat Deformation Functor (1997) (15)
- Reductive Group Schemes (sga3 Summer School, 2011) (2011) (13)
- Modular curves and Ramanujan's continued fraction (2006) (13)
- Impossibility theorems for elementary integration (2005) (12)
- DESCENT FOR COHERENT SHEAVES ON RIGID-ANALYTIC SPACES (2004) (11)
- AN OVERVIEW OF A THEOREM OF FLACH (2003) (11)
- THE STRUCTURE OF SOLVABLE GROUPS OVER GENERAL FIELDS (2011) (11)
- FORMAL GAGA ON ARTIN STACKS (2005) (11)
- RELATIVE AMPLENESS IN RIGID-ANALYTIC GEOMETRY (2006) (9)
- Descent for nonarchimedean analytic spaces (2019) (9)
- Inertia groups and fibers (2000) (8)
- Classification of Pseudo-reductive Groups (AM-191) (2015) (7)
- FINITENESS OF CLASS NUMBERS FOR ALGEBRAIC GROUPS (2006) (7)
- Structure and classification of pseudo-reductive groups (2017) (6)
- SEMISTABLE REDUCTION FOR ABELIAN VARIETIES (2011) (5)
- CM lifting of abelian varieties up to isogeny (2013) (4)
- Pseudo-reductive Groups: Contents (2010) (4)
- MOISHEZON SPACES IN RIGID GEOMETRY (2010) (4)
- UNIVERSAL PROPERTY OF NON-ARCHIMEDEAN ANALYTIFICATION (2010) (4)
- CLARIFICATONS AND CORRECTIONS FOR GROTHENDIECK DUALITY AND BASE CHANGE (2004) (4)
- Prime specialization in higher genus I (2008) (3)
- Finite Honda systems and supersingular elliptic curves (1996) (2)
- MAIN THEOREM OF COMPLEX MULTIPLICATION (2006) (2)
- étale cohomology of algebraic number fields (2016) (2)
- Finite-order automorphisms of a certain torus (2004) (1)
- Has Connected Fibers (2003) (1)
- CLASSICAL MOTIVATION FOR THE RIEMANN–HILBERT CORRESPONDENCE (2006) (1)
- The Möbius function and the residue theorem (2005) (1)
- Gabber ’ s lemma (2011) (1)
- THE TRACE FORMULA FOR COMPACT QUOTIENTS JEREMY BOOHER WITH AN APPENDIX BY BRIAN CONRAD (2014) (1)
- Survey of Kisin's Paper Crystalline Representations and F -crystals (2008) (1)
- Survey of Kisin's Paper Crystalline Representations and F -crystals (2008) (1)
- Néron models, Tamagawa factors, and Tate-Shafarevich groups (2015) (1)
- Proof of Main Theorem (2000) (1)
- NON-SPLIT REDUCTIVE GROUPS OVER Z Brian Conrad (2014) (0)
- Pseudo-reductive Groups: Variation of ( G ′, k ′/ k, T ′, C ) (2010) (0)
- Pseudo-reductive Groups: Tits' work on unipotent groups in nonzero characteristic (2010) (0)
- Current Trends in Arithmetic Geometry and Number Theory (0)
- CM lifting of -divisible groups (2013) (0)
- Pseudo-reductive Groups: The exotic constructions (2010) (0)
- Pseudo-reductive Groups: Overview of pseudo-reductivity (2010) (0)
- B. Clifford constructions (2015) (0)
- 7. Constructions with regular degenerate quadratic forms (2015) (0)
- OVERVIEW OF MORET-BAILLY’S THEOREM ON GLOBAL POINTS (2006) (0)
- Editorial comment. The GCHQ Problem Solving Group counted F via the Priifer cor- respondence and the inclusion-exclusion principle: (2016) (0)
- CM lifting via -adic Hodge theory (2013) (0)
- Pseudo-reductive Groups: References (2010) (0)
- Artin-Tate Conjecture , fibered surfaces , and minimal regular proper model (2015) (0)
- Erratum to "Modular curves and Ramanujan's continued fraction" (2008) (0)
- Pseudo-reductive groups and their arithmetic applications (mini-course, lecture 1) (2013) (0)
- Pseudo-reductive Groups: General case (2010) (0)
- 4. Central extensions and groups locally of minimal type (2015) (0)
- C. Pseudo-split and quasi-split forms (2015) (0)
- A BRIEF INTODUCTION TO ADIC SPACES (2018) (0)
- Fermat ’ s Last Theorem After 356 (2007) (0)
- Pseudo-reductive Groups: Basic structure theory (2010) (0)
- Pseudo-reductive Groups: Applications (2010) (0)
- SOME FINITENESS THEOREMS FOR ABELIAN VARIETIES (2011) (0)
- The absolutely pseudo-simple groups in characteristic 2 (2010) (0)
- Pseudo-reductive Groups: Rational conjugacy in connected groups (2010) (0)
- CHAPTER 2 Several approaches to non-archimedean geometry (2007) (0)
- A. Pseudo-isogenies (2015) (0)
- Pi and Rationals: 10961 (2004) (0)
- 5. Universal smooth k-tame central extension (2015) (0)
- Pseudo-reductive Groups: Ubiquity of the standard construction (2010) (0)
- 3. Field-theoretic and linear-algebraic invariants (2015) (0)
- Pseudo-reductive Groups: Terminology, conventions, and notation (2010) (0)
- CORRECTIONS TO \INERTIA GROUPS AND FIBERS" (1997) (0)
- Some arithmetic results for abelian varieties (2013) (0)
- Pseudo-reductive Groups: Background in linear algebraic groups (2010) (0)
- Remarks on mod-ln Representations, l=3, 5 (1999) (0)
- 6. Automorphisms, isomorphisms, and Tits classification (2015) (0)
- CM lifting over a discrete valuation ring (2013) (0)
- GRUNWALD – WANG FOR GLOBAL CHARACTER GROUPS (2010) (0)
- D. Basic exotic groups of type F4 of relative rank 2 (2015) (0)
- Rational conjugacy and relative root systems (2015) (0)
- Algebraic theory of complex multiplication (2013) (0)
- 9. Generalization of the standard construction (2015) (0)
- Titles and Abstracts (2013) (0)
- Pseudo-reductive groups and their arithmetic applications (mini-course, lecture 2) (2013) (0)
- INTODUCTION TO ADIC SPACES BRIAN (2018) (0)
- 8. Constructions when Φ has a double bond (2015) (0)
- The Fermat–euler Theorem V.10 Fermat's Last Theorem V.11 Fixed Point Theorems (0)
- Pseudo-reductive Groups: Root groups and root systems (2010) (0)
- 2. Preliminary notions (2015) (0)
- Preparations for classification in characteristics 2 and 3 (2010) (0)
- NON-SPLIT REDUCTIVE GROUPS OVER Z Brian Conrad (2014) (0)

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## What Schools Are Affiliated With Brian Conrad?

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