James Milne | Academic Influence

James Milne 's AcademicInfluence.com Rankings

James Milne

Mathematics

#1932

World Rank

#3064

Historical Rank

Measure Theory

#1627

World Rank

#2007

Historical Rank

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Mathematics

James Milne 's Degrees

PhD Mathematics University of Auckland
Bachelors Mathematics University of Auckland

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Why Is James Milne Influential?

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According to Wikipedia, James S. Milne is a New Zealand mathematician working in arithmetic geometry. Life Milne attended the High School in Invercargill in New Zealand until 1959, and then studied at the University of Otago in Dunedin and Harvard University . From then to 1969 he was a lecturer at University College London. After that he was at the University of Michigan, as Assistant Professor , Associate Professor , Professor , and Professor Emeritus . He has also been a visiting professor at King's College London, at the Institut des hautes études scientifiques in Paris , at the Mathematical Sciences Research Institute in Berkeley, California , and the Institute for Advanced Study in Princeton, New Jersey .

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James Milne 's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Hodge Cycles, Motives, and Shimura Varieties (1989) (1011)
Arithmetic Duality Theorems (1987) (951)
Elliptic Curves (2020) (502)
Class Field Theory (2013) (328)
Tannakian Categories (2012) (290)
Algebraic Groups: The Theory of Group Schemes of Finite Type over a Field (2017) (270)
Introduction to Shimura Varieties (2004) (235)
Canonical Models of (Mixed) Shimura Varieties and Automorphic Vector Bundles (2002) (206)
On a conjecture of Artin and Tate (1975) (189)
On the arithmetic of abelian varieties (1972) (177)
VALUES OF ZETA FUNCTIONS OF VARIETIES OVER FINITE FIELDS (1986) (140)
The points on a Shimura variety modulo a prime of good reduction (1992) (126)
Etale Cohomology (PMS-33) (1980) (121)
Giant piezoresistance effects in silicon nanowires and microwires. (2010) (117)
Reductive Groups (2012) (109)
Duality in the flat cohomology of a surface (1976) (81)
Shimura Varieties and Motives (2001) (75)
MOTIVES OVER FINITE FIELDS (1994) (73)
The Action of an Automorphism of C On a Shimura Variety and its Special Points (1983) (72)
Lectures on etale cohomology (2008) (60)
Algebraic Number Theory (1992) (57)
Zero cycles on algebraic varieties in nonzero characteristic : Rojtman's theorem (1982) (57)
The Tate-Šafarevič group of a constant abelian variety (1968) (52)
Conjugates of Shimura Varieties (1982) (52)
Lefschetz classes on abelian varieties (1999) (48)
Automorphic Forms, Shimura Varieties and L-Functions: Proceedings of a Conference Held at the University of Michigan, Ann Arbor, July 6-16, 1988 (1990) (47)
Shimura Varieties and Moduli (2011) (41)
Motivic cohomology and values of zeta functions (1988) (40)
Erratum: Tannakian Categories (1982) (37)
Algebraic Groups , Lie Groups , and their Arithmetic Subgroups (2010) (32)
Comparison of the Brauer group with the Tate-Safarevic group (1982) (31)
Lefschetz Motives and the Tate Conjecture (1999) (31)
Duality in the flat cohomology of curves (1976) (30)
Langlands’s Construction of the Taniyama Group (1982) (28)
The Tate conjecture over finite fields (AIM talk) (2007) (26)
Automorphic vector bundles on connected Shimura varieties (1988) (24)
Points on Shimura varieties over finite fields: the conjecture of Langlands and Rapoport (2007) (24)
The Tate Conjecture for Certain Abelian Varieties over Finite Fields (1999) (24)
Nonhomeomorphic conjugates of connected Shimura varieties (2008) (23)
Weil-Châtelet groups over local fields (1970) (23)
Descent for Shimura varieties. (1997) (23)
Polarizations and Grothendieck's Standard Conjectures (2001) (23)
Integral motives and special values of zeta functions (2002) (22)
The Brauer group of a rational surface (1970) (22)
The Riemann Hypothesis over Finite Fields: From Weil to the Present Day (2015) (21)
Motives — Grothendieck’s Dream (2012) (21)
Piezoresistance in silicon at uniaxial compressive stresses up to 3 GPa. (2010) (21)
Extensions of abelian varieties defined over a finite field (1968) (17)
Abelian Varieties (2000) (17)
The action of complex conjugation on a Shimura variety (1981) (15)
Gerbes and abelian motives (2003) (15)
Elements of Order P in the Tate-šafarevič Group (1970) (14)
The conjecture of Langlands and Rapoport for Siegel modular varieties (1991) (14)
QUOTIENTS OF TANNAKIAN CATEGORIES (2005) (14)
Automorphism Groups of Shimura Varieties and Reciprocity Laws (1981) (14)
The Homological Dimension of Commutative Group Schemes over a Perfect Field (1970) (13)
Canonical models of Shimura curves (2003) (11)
Abelian varieties defined over their Fields of Moduli, I† (1972) (10)
Rational Tate classes (2007) (10)
The Fundamental Theorem of Complex Multiplication (2007) (9)
Finite Group Schemes (2017) (9)
Notations and Conventions (1982) (8)
Motivic complexes and special values of zeta functions (2013) (8)
A Proof of the Barsotti-Chevalley Theorem on Algebraic Groups (2013) (8)
Abelian varieties with complex multiplication (for pedestrians) (1998) (7)
Kazhdan's Theorem on Arithmetic Varieties (2001) (7)
THE p-COHOMOLOGY OF ALGEBRAIC VARIETIES AND SPECIAL VALUES OF ZETA FUNCTIONS (2013) (6)
Semisimple Lie Algebras, Algebraic Groups, and Tensor Categories (2007) (6)
Semisimple Algebraic Groups in Characteristic Zero (2007) (5)
Group Theory (2003) (5)
Rational Tate classes on abelian varieties (2007) (5)
A Primer of Commutative Algebra (2009) (5)
Correction: Abelian Varieties defined over their Fields of Moduli, I (1974) (4)
What is a Motive (2009) (4)
Motivic complexes over finite fields and the ring of correspondences at the generic point (2006) (4)
Addendum to “Values of zeta functions of varieties over finite fields” (2015) (4)
On the conjecture of Langlands and Rapoport (2007) (4)
The de Rham-Witt and Z p -cohomologies of an algebraic variety (2005) (3)
The Work of John Tate (2012) (3)
Some estimates from étale cohomology. (1981) (2)
TOWARDS A PROOF OF THE CONJECTURE OF LANGLANDS AND RAPOPORT (2007) (2)
Weil-Châtelet groups over local fields : addendum (1972) (2)
SHIMURA VARIETIES: THE GEOMETRIC SIDE OF THE ZETA FUNCTION (1995) (2)
Periods of abelian varieties (2002) (2)
The (failure of the) Hasse principle for centres of semisimple groups (2017) (1)
Addendum to: Milne, Values of zeta functions of varieties over finite fields, Amer. J. Math. 108, (1986), 297-360 (2012) (1)
On a Theorem of Mazur and Roberts (1973) (1)
Addendum / Erratum for Arithmetic Duality Theorems (2018) (1)
Erratum: Conjugates of Shimura Varieties (1982) (1)
On the Tate and Standard Conjectures over Finite Fields (2019) (1)
Classification of the Mumford--Tate Groups of Rational Polarizable Hodge Structures (2020) (1)
The Structure of Solvable Algebraic Groups (2017) (1)
Hodge classes on abelian varieties (2020) (1)
Numerical and homological equivalence over finite fields (2019) (0)
Tannaka Duality; Jordan Decompositions (2017) (0)
What is... a Shimura variety (2012) (0)
Groups of Multiplicative Type; Linearly Reductive Groups (2017) (0)
Subnormal Series; Solvable and Nilpotent Algebraic Groups (2017) (0)
Appendix B. Spectral Sequences (1980) (0)
Construction of the Semisimple Groups (2017) (0)
Review of Algebraic Geometry (2017) (0)
The Conjectures of Grothendieck, Hodge, and Tate for Abelian varieties (2021) (0)
Vi Arithmetic Subgroups (0)
Chapter I. Étale Morphisms (1980) (0)
Linear Representations of Algebraic Groups (2017) (0)
Unipotent Algebraic Groups (2017) (0)
Chapter III. Cohomology (1980) (0)
Appendix A. Limits (1980) (0)
Erratum: Notations and Conventions (1982) (0)
Cohomology and Extensions (2017) (0)
Review of : Shimura , Collected Papers (2004) (0)
Definitions and Basic Properties (2017) (0)
Affine Algebraic Groups and Hopf Algebras (2017) (0)
Review of the Collected Works of John Tate (2017) (0)
The Geometry of Algebraic Groups (2017) (0)
Erratum: General Introduction (1982) (0)
Appendix C. Hypercohomology (1980) (0)
Ju l 2 00 7 Quotients of Tannakian Categories (0)
Erratum: Langlands’s Construction of the Taniyama Group (1982) (0)
Book Reviews (1986) (0)
The Structure of General Algebraic Groups (2017) (0)
Representations of Reductive Groups (2017) (0)
Motives over F_p (2006) (0)
Algebraic groups as automorphism groups of algebras. (2020) (0)
Split Reductive Groups (2017) (0)
Existence of Quotients of Algebraic Groups (2017) (0)
Semisimple and Reductive Groups (2017) (0)
Chapter V. The Cohomology of Curves and Surfaces (1980) (0)
The Works of John Tate [reprinted from J. S. Milne, “The Works of John Tate”, The Abel Prize 2008–2012, (Helge Holden and Ragni Piene, editors), pp. 259–340 Springer, Heidelberg, 2014.] (2017) (0)
Algebraic Groups Acting on Schemes (2017) (0)
Chapter IV. The Brauer Group (1980) (0)
of the Collected Works of John Tate (2017) (0)
ul 2 00 7 Rational Tate classes on abelian varieties (0)
Tori Acting on Schemes (2017) (0)
Lie Groups (0)
Study of an Isogeny Class (2002) (0)
Chapter VI. The Fundamental Theorems (1980) (0)
The Lie Algebra of an Algebraic Group (2017) (0)
Addendum/Erratum for Arithmetic Duality Theorems 2nd edition 2006 (2014) (0)
Terminology and Conventions (1980) (0)
Jacobian Varieties (2021) (0)
Review of SGA 3 ( 2011 edition ) , (2012) (0)
Taxonomy Working Group Final Report (2013) (0)
Examples and Basic Constructions (2017) (0)
A G ] 13 A pr 2 00 8 Nonhomeomorphic conjugates of connected Shimura varieties (2021) (0)
Grothendieck's standard conjecture of Lefschetz type over finite fields (2020) (0)
Algebraic Groups over Arbitrary Fields (2010) (0)
Chapter II. Sheaf Theory (1980) (0)
Group Theory; the Isomorphism Theorems (2017) (0)
Borel Subgroups and Applications (2017) (0)
The Isogeny and Existence Theorems (2017) (0)
Algebraic Groups of Semisimple Rank One (2017) (0)

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