Milne, J. S. 1942
Overview
Works:  51 works in 148 publications in 3 languages and 1,873 library holdings 

Genres:  Conference papers and proceedings Longitudinal studies Poetry 
Roles:  Author, Editor 
Classifications:  QA564, 516.35 
Publication Timeline
.
Most widely held works by
J. S Milne
Étale cohomology by
J. S Milne(
Book
)
22 editions published between 1979 and 2017 in English and Russian and held by 685 WorldCat member libraries worldwide
One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced étale cohomology in order to extend the methods of sheaftheoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry, but also in several different branches of number theory and in the representation theory of finite and padic groups. Yet until now, the work has been available only in the original massive and difficult papers. In order to provide an accessible introduction to étale cohomology, J. S. Milne offers this more elementary account covering the essential features of the theory. The author begins with a review of the basic properties of flat and étale morphisms and of the algebraic fundamental group. The next two chapters concern the basic theory of étale sheaves and elementary étale cohomology, and are followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Professor Milne proves the fundamental theorems in étale cohomology  those of base change, purity, Poincaré duality, and the Lefschetz trace formula. He then applies these theorems to show the rationality of some very general Lseries
22 editions published between 1979 and 2017 in English and Russian and held by 685 WorldCat member libraries worldwide
One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced étale cohomology in order to extend the methods of sheaftheoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry, but also in several different branches of number theory and in the representation theory of finite and padic groups. Yet until now, the work has been available only in the original massive and difficult papers. In order to provide an accessible introduction to étale cohomology, J. S. Milne offers this more elementary account covering the essential features of the theory. The author begins with a review of the basic properties of flat and étale morphisms and of the algebraic fundamental group. The next two chapters concern the basic theory of étale sheaves and elementary étale cohomology, and are followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Professor Milne proves the fundamental theorems in étale cohomology  those of base change, purity, Poincaré duality, and the Lefschetz trace formula. He then applies these theorems to show the rationality of some very general Lseries
Arithmetic duality theorems by
J. S Milne(
Book
)
10 editions published between 1986 and 2006 in English and held by 335 WorldCat member libraries worldwide
10 editions published between 1986 and 2006 in English and held by 335 WorldCat member libraries worldwide
Automorphic forms, Shimura varieties, and Lfunctions : proceedings of a conference held at the University of Michigan, Ann
Arbor, July 616, 1988(
Book
)
15 editions published between 1989 and 1990 in English and Multiple languages and held by 198 WorldCat member libraries worldwide
15 editions published between 1989 and 1990 in English and Multiple languages and held by 198 WorldCat member libraries worldwide
Algebraic groups : the theory of group schemes of finite type over a field by
J. S Milne(
Book
)
9 editions published in 2017 in English and held by 167 WorldCat member libraries worldwide
"Algebraic groups play much the same role for algebraists as Lie groups play for analysts. This book is the first comprehensive introduction to the theory of algebraic group schemes over fields that includes the structure theory of semisimple algebraic groups, and is written in the language of modern algebraic geometry. The first eight chapters study general algebraic group schemes over a field and culminate in a proof of the BarsottiChevalley theorem, realizing every algebraic group as an extension of an abelian variety by an affine group. After a review of the Tannakian philosophy, the author provides short accounts of Lie algebras and finite group schemes. The later chapters treat reductive algebraic groups over arbitrary fields, including the BorelChevalley structure theory. Solvable algebraic groups are studied in detail. Prerequisites have also been kept to a minimum so that the book is accessible to nonspecialists in algebraic geometry."  publisher
9 editions published in 2017 in English and held by 167 WorldCat member libraries worldwide
"Algebraic groups play much the same role for algebraists as Lie groups play for analysts. This book is the first comprehensive introduction to the theory of algebraic group schemes over fields that includes the structure theory of semisimple algebraic groups, and is written in the language of modern algebraic geometry. The first eight chapters study general algebraic group schemes over a field and culminate in a proof of the BarsottiChevalley theorem, realizing every algebraic group as an extension of an abelian variety by an affine group. After a review of the Tannakian philosophy, the author provides short accounts of Lie algebras and finite group schemes. The later chapters treat reductive algebraic groups over arbitrary fields, including the BorelChevalley structure theory. Solvable algebraic groups are studied in detail. Prerequisites have also been kept to a minimum so that the book is accessible to nonspecialists in algebraic geometry."  publisher
Clinical effects of ageing : a longitudinal study by
J. S Milne(
Book
)
5 editions published in 1985 in English and Undetermined and held by 134 WorldCat member libraries worldwide
5 editions published in 1985 in English and Undetermined and held by 134 WorldCat member libraries worldwide
Hodge cycles, motives, and Shimura varieties by
Pierre Deligne(
)
11 editions published between 1981 and 1989 in English and held by 84 WorldCat member libraries worldwide
11 editions published between 1981 and 1989 in English and held by 84 WorldCat member libraries worldwide
Microcomputer applications in measurement systems by
Charles Fraser(
Book
)
5 editions published in 1990 in English and held by 84 WorldCat member libraries worldwide
5 editions published in 1990 in English and held by 84 WorldCat member libraries worldwide
Elliptic curves by
J. S Milne(
Book
)
9 editions published between 1996 and 2006 in English and held by 79 WorldCat member libraries worldwide
This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis and topology usually taught in advanced undergraduate or firstyear graduate courses
9 editions published between 1996 and 2006 in English and held by 79 WorldCat member libraries worldwide
This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis and topology usually taught in advanced undergraduate or firstyear graduate courses
Arithmetic duality theorems by
J. S Milne(
Book
)
5 editions published in 1986 in English and Undetermined and held by 29 WorldCat member libraries worldwide
5 editions published in 1986 in English and Undetermined and held by 29 WorldCat member libraries worldwide
ALGEBRAIC GROUPS : the theory of algebraic group schemes over fields by
J. S Milne(
Book
)
1 edition published in 2017 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 2017 in English and held by 8 WorldCat member libraries worldwide
A longitudinal study of ageing persons by
J. S Milne(
Book
)
4 editions published between 1981 and 1982 in English and held by 5 WorldCat member libraries worldwide
4 editions published between 1981 and 1982 in English and held by 5 WorldCat member libraries worldwide
The poetry of John Milne : poems of the North East in the Aberdeenshire dialect : extract from an original text published
in 1900 by
J. S Milne(
Book
)
1 edition published in 1995 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 1995 in English and held by 5 WorldCat member libraries worldwide
Arithmetic geometry by
Gary Cornell(
)
1 edition published in 1986 in English and held by 4 WorldCat member libraries worldwide
This book is the result of a conference on arithmetic geometry, held July 30 through August 10, 1984 at the University of Connecticut at Storrs, the purpose of which was to provide a coherent overview of the subject. This subject has enjoyed a resurgence in popularity due in part to Faltings' proof of Mordell's conjecture. Included are extended versions of almost all of the instructional lectures and, in addition, a translation into English of Faltings' groundbreaking paper. ARITHMETIC GEOMETRY should be of great use to students wishing to enter this field, as well as those already working in it. This revised second printing now includes a comprehensive index
1 edition published in 1986 in English and held by 4 WorldCat member libraries worldwide
This book is the result of a conference on arithmetic geometry, held July 30 through August 10, 1984 at the University of Connecticut at Storrs, the purpose of which was to provide a coherent overview of the subject. This subject has enjoyed a resurgence in popularity due in part to Faltings' proof of Mordell's conjecture. Included are extended versions of almost all of the instructional lectures and, in addition, a translation into English of Faltings' groundbreaking paper. ARITHMETIC GEOMETRY should be of great use to students wishing to enter this field, as well as those already working in it. This revised second printing now includes a comprehensive index
Arithmetic duality theorems by
J. S Milne(
Book
)
1 edition published in 1986 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1986 in English and held by 3 WorldCat member libraries worldwide
Class field theory : v3.1 by
J. S Milne(
Book
)
3 editions published between 1997 and 2011 in English and held by 3 WorldCat member libraries worldwide
3 editions published between 1997 and 2011 in English and held by 3 WorldCat member libraries worldwide
Automorphic forms, Shimura varieties, and lfunctions(
Book
)
1 edition published in 1990 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1990 in English and held by 3 WorldCat member libraries worldwide
Algebraic number theory : v2.10 by
J. S Milne(
Book
)
3 editions published between 1998 and 2012 in English and held by 3 WorldCat member libraries worldwide
3 editions published between 1998 and 2012 in English and held by 3 WorldCat member libraries worldwide
Lectures on etale cohomology : v2.01 by
J. S Milne(
Book
)
2 editions published between 1998 and 2012 in English and held by 2 WorldCat member libraries worldwide
2 editions published between 1998 and 2012 in English and held by 2 WorldCat member libraries worldwide
The conjecture of Birch and SwinnertonDyer for constant abelian varieties over function fields by
J. S Milne(
Book
)
2 editions published in 1967 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1967 in English and held by 2 WorldCat member libraries worldwide
Etale cohomology (pms33) by
J. S Milne(
Book
)
1 edition published in 2016 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2016 in English and held by 2 WorldCat member libraries worldwide
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Associated Subjects
Abelian varieties Age factors in disease Algebraic fields Algebraic number theory Arithmetical algebraic geometry Automorphic forms Categories (Mathematics) Class field theory Curves, Elliptic Demography Duality theory (Mathematics) Geometry Geometry, Algebraic Geriatrics Group theory Homology theory Human services Lfunctions Linear algebraic groups Mathematics MeasurementData processing MicrocomputersProgramming Scotland Sheaf theory Shimura varieties Sociology Varieties (Universal algebra) Weil conjectures
Covers
Alternative Names
J.S.ミルン
James Milne matemático neozelandés
James Milne mathématicien néozélandais
James Milne neuseeländischer Mathematiker
James Milne wiskundige uit NieuwZeeland
Miln, Dž.
Miln, Dž 1942
Miln, Džejms.
Milne, J. S.
Milne, J. S. 1942
Milne, James S. 1942
Джеймс Милн математик
Милн Дж.
جيمس ميلن
جيمس ميلن رياضياتي نيوزيلندي
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