Deligne, Pierre
Overview
Works:  161 works in 402 publications in 5 languages and 3,717 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Collector, Other, Opponent, Interviewee, Contributor, Commentator, Creator, Director 
Classifications:  QA3, 530.143 
Publication Timeline
.
Most widely held works by
Pierre Deligne
Hodge cycles, motives, and Shimura varieties by
Pierre Deligne(
Book
)
31 editions published between 1981 and 2008 in 3 languages and held by 641 WorldCat member libraries worldwide
31 editions published between 1981 and 2008 in 3 languages and held by 641 WorldCat member libraries worldwide
Équations différentielles à points singuliers réguliers by
Pierre Deligne(
Book
)
27 editions published between 1970 and 2008 in 4 languages and held by 596 WorldCat member libraries worldwide
27 editions published between 1970 and 2008 in 4 languages and held by 596 WorldCat member libraries worldwide
Commensurabilities among lattices in PU (1,n) by
Pierre Deligne(
Book
)
15 editions published between 1993 and 2016 in English and Undetermined and held by 545 WorldCat member libraries worldwide
The first part of this monograph is devoted to a characterization of hypergeometriclike functions, that is, twists of hypergeometric functions in nvariables. These are treated as an (n+1) dimensional vector space of multivalued locally holomorphic functions defined on the space of n+3 tuples of distinct points on the projective line P modulo, the diagonal section of Auto P=m. For n=1, the characterization may be regarded as a generalization of Riemann's classical theorem characterizing hypergeometric functions by their exponents at three singular points. This characterization permits the authors to compare monodromy groups corresponding to different parameters and to prove commensurability modulo inner automorphisms of PU(1,n). The book includes an investigation of elliptic and parabolic monodromy groups, as well as hyperbolic monodromy groups. The former play a role in the proof that a surprising number of lattices in PU(1,2) constructed as the fundamental groups of compact complex surfaces with constant holomorphic curvature are in fact conjugate to projective monodromy groups of hypergeometric functions. The characterization of hypergeometriclike functions by their exponents at the divisors "at infinity" permits one to prove generalizations in nvariables of the Kummer identities for n1 involving quadratic and cubic changes of the variable
15 editions published between 1993 and 2016 in English and Undetermined and held by 545 WorldCat member libraries worldwide
The first part of this monograph is devoted to a characterization of hypergeometriclike functions, that is, twists of hypergeometric functions in nvariables. These are treated as an (n+1) dimensional vector space of multivalued locally holomorphic functions defined on the space of n+3 tuples of distinct points on the projective line P modulo, the diagonal section of Auto P=m. For n=1, the characterization may be regarded as a generalization of Riemann's classical theorem characterizing hypergeometric functions by their exponents at three singular points. This characterization permits the authors to compare monodromy groups corresponding to different parameters and to prove commensurability modulo inner automorphisms of PU(1,n). The book includes an investigation of elliptic and parabolic monodromy groups, as well as hyperbolic monodromy groups. The former play a role in the proof that a surprising number of lattices in PU(1,2) constructed as the fundamental groups of compact complex surfaces with constant holomorphic curvature are in fact conjugate to projective monodromy groups of hypergeometric functions. The characterization of hypergeometriclike functions by their exponents at the divisors "at infinity" permits one to prove generalizations in nvariables of the Kummer identities for n1 involving quadratic and cubic changes of the variable
Quantum fields and strings : a course for mathematicians(
Book
)
35 editions published between 1999 and 2000 in English and Undetermined and held by 459 WorldCat member libraries worldwide
35 editions published between 1999 and 2000 in English and Undetermined and held by 459 WorldCat member libraries worldwide
Cohomologie étale by
Pierre Deligne(
Book
)
7 editions published in 1977 in French and Undetermined and held by 420 WorldCat member libraries worldwide
7 editions published in 1977 in French and Undetermined and held by 420 WorldCat member libraries worldwide
Cohomologie étale Séminaire de géometrie algébrique du Bois Marie SGA 4 1/2 by
Pierre Deligne(
Book
)
27 editions published between 1974 and 2009 in 4 languages and held by 131 WorldCat member libraries worldwide
27 editions published between 1974 and 2009 in 4 languages and held by 131 WorldCat member libraries worldwide
Modular functions of one variable, IIV: proceedings, International Summer School, University of Antwerp, RUCA, July 17August
3, 1972 by
International Summer School on Modular Functions(
)
in English and held by 125 WorldCat member libraries worldwide
in English and held by 125 WorldCat member libraries worldwide
Singularités irrégulières : correspondance et documents by
Pierre Deligne(
Book
)
12 editions published between 2007 and 2008 in French and held by 108 WorldCat member libraries worldwide
12 editions published between 2007 and 2008 in French and held by 108 WorldCat member libraries worldwide
Modular functions of one variable : proceedings, international summer school, University of Antwerp, RUCA, July 17  August
3, 1972 by
Pierre Deligne(
Book
)
11 editions published between 1973 and 1986 in English and held by 53 WorldCat member libraries worldwide
11 editions published between 1973 and 1986 in English and held by 53 WorldCat member libraries worldwide
Groupes de monodromie en géométrie algébrique [2] : Séminaire de géométrie agébrique du BoisMarie 19671969. (SGA
7 II)(
Book
)
1 edition published in 1973 in French and held by 43 WorldCat member libraries worldwide
1 edition published in 1973 in French and held by 43 WorldCat member libraries worldwide
Modular functions of one variable II : proceedings of the international summer school University of Antwerp RUCA by International Summer School on Modular Functions of One Variable(
Book
)
1 edition published in 1973 in English and held by 36 WorldCat member libraries worldwide
1 edition published in 1973 in English and held by 36 WorldCat member libraries worldwide
Modular Functions of One Variable II : Proceedings International Summer School University of Antwerp, RUCA July 17August
3, 1972 by
Pierre Deligne(
)
2 editions published in 1973 in English and held by 32 WorldCat member libraries worldwide
2 editions published in 1973 in English and held by 32 WorldCat member libraries worldwide
Théorie de Hodge, II by
Pierre Deligne(
Book
)
8 editions published between 1971 and 1972 in French and English and held by 28 WorldCat member libraries worldwide
8 editions published between 1971 and 1972 in French and English and held by 28 WorldCat member libraries worldwide
Théorie de Hodge : 3. Groups of simple algebras / by Moss E. Sweedler [u.a.] by
Pierre Deligne(
Book
)
14 editions published between 1972 and 1975 in 3 languages and held by 28 WorldCat member libraries worldwide
14 editions published between 1972 and 1975 in 3 languages and held by 28 WorldCat member libraries worldwide
Groupes de monodromie en géométrie algébrique by Séminaire de géometrie algébrique(
Book
)
3 editions published in 1972 in French and held by 22 WorldCat member libraries worldwide
3 editions published in 1972 in French and held by 22 WorldCat member libraries worldwide
Théorie des topos et cohomologie étale des schémas. [Séminaire de géométrie algébrique du BoisMarie 1963/64  SGA
4] by
Michael Artin(
Book
)
4 editions published between 1972 and 1973 in French and held by 20 WorldCat member libraries worldwide
4 editions published between 1972 and 1973 in French and held by 20 WorldCat member libraries worldwide
Commensurabilities among Lattices in PU (1,n). (AM132) by
Pierre Deligne(
)
1 edition published in 2016 in English and held by 19 WorldCat member libraries worldwide
The first part of this monograph is devoted to a characterization of hypergeometriclike functions, that is, twists of hypergeometric functions in nvariables. These are treated as an (n+1) dimensional vector space of multivalued locally holomorphic functions defined on the space of n+3 tuples of distinct points on the projective line P modulo, the diagonal section of Auto P=m. For n=1, the characterization may be regarded as a generalization of Riemann's classical theorem characterizing hypergeometric functions by their exponents at three singular points. This characterization permits the authors to compare monodromy groups corresponding to different parameters and to prove commensurability modulo inner automorphisms of PU(1,n). The book includes an investigation of elliptic and parabolic monodromy groups, as well as hyperbolic monodromy groups. The former play a role in the proof that a surprising number of lattices in PU(1,2) constructed as the fundamental groups of compact complex surfaces with constant holomorphic curvature are in fact conjugate to projective monodromy groups of hypergeometric functions. The characterization of hypergeometriclike functions by their exponents at the divisors "at infinity" permits one to prove generalizations in nvariables of the Kummer identities for n1 involving quadratic and cubic changes of the variable
1 edition published in 2016 in English and held by 19 WorldCat member libraries worldwide
The first part of this monograph is devoted to a characterization of hypergeometriclike functions, that is, twists of hypergeometric functions in nvariables. These are treated as an (n+1) dimensional vector space of multivalued locally holomorphic functions defined on the space of n+3 tuples of distinct points on the projective line P modulo, the diagonal section of Auto P=m. For n=1, the characterization may be regarded as a generalization of Riemann's classical theorem characterizing hypergeometric functions by their exponents at three singular points. This characterization permits the authors to compare monodromy groups corresponding to different parameters and to prove commensurability modulo inner automorphisms of PU(1,n). The book includes an investigation of elliptic and parabolic monodromy groups, as well as hyperbolic monodromy groups. The former play a role in the proof that a surprising number of lattices in PU(1,2) constructed as the fundamental groups of compact complex surfaces with constant holomorphic curvature are in fact conjugate to projective monodromy groups of hypergeometric functions. The characterization of hypergeometriclike functions by their exponents at the divisors "at infinity" permits one to prove generalizations in nvariables of the Kummer identities for n1 involving quadratic and cubic changes of the variable
Quantum fields and strings : a course for mathematicians(
Book
)
8 editions published between 1945 and 2000 in English and Undetermined and held by 19 WorldCat member libraries worldwide
8 editions published between 1945 and 2000 in English and Undetermined and held by 19 WorldCat member libraries worldwide
Monodromy of hypergeometric functions and nonlattice integral monodromy by
Pierre Deligne(
Book
)
6 editions published between 1983 and 1986 in English and held by 17 WorldCat member libraries worldwide
6 editions published between 1983 and 1986 in English and held by 17 WorldCat member libraries worldwide
Central extensions of reductive groups by K₂ by
J.L Brylinski(
Book
)
5 editions published in 2001 in English and held by 17 WorldCat member libraries worldwide
5 editions published in 2001 in English and held by 17 WorldCat member libraries worldwide
more
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Audience Level
0 

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Kids  General  Special 
Related Identities
 Mostow, George D. Contributor Editor
 Institute for Advanced Study (Princeton, N.J.)
 Kuyk, Willem Author Editor
 Serre, JeanPierre 1926 Interviewee Editor
 Birch, B. J. (Bryan John) Editor
 Katz, N. Other Director Editor
 Malgrange, B. (Bernard)
 Ramis, J.P (JeanPierre)
 Grothendieck, Alexandre (19282014) Other Editor
 Milne, James S.
Useful Links
Associated Subjects
Abelian varieties Algebra Algebraic varieties Asymptotes Belgium Bourgain, Jean, C*algebras Calculus of residues Categories (Mathematics) Connections (Mathematics) Convolutions (Mathematics) Daubechies, Ingrid Differential equations Differential equations, Linear Functor theory Geometry, Algebraic Global analysis (Mathematics) Group theory Homology theory Hypergeometric functions Ktheory Lattice theory Mathematical physics Mathematicians Mathematics Modular functions Monodromy groups Number theory Quantum field theory Sheaf theory Singularities (Mathematics) String models Topology Toposes
Covers
Alternative Names
Deligne, P.
Deligne, P. 1944
Deligne, P. (Pierre)
Deligne, Pierre.
Deligne, Pierre R. 1944
Pierre Deligne Belgisch wiskundige
Pierre Deligne belgischer Mathematiker
Pierre Deligne belgisk matematikar
Pierre Deligne belgisk matematiker
Pierre Deligne matemático belga
Pierre Deligne mathematician
Pierre Deligne mathématicien
Pierre René Deligne
Пиер Делин
Пьер Делинь математик
П'єр Рене Делінь
פייר דלין
بيار ديلين
پیر دلین ریاضیدان بلژیکی
پیری ڈلیگن
پییر دلین
ဖြဲ ဒဲလိည
피에르 들리뉴
ピエール・ルネ・ドリーニュ
皮埃尔·德利涅
Languages