WorldCat Identities

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
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Most widely held works about Pierre Deligne
 
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

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

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 hypergeometric-like functions, that is, twists of hypergeometric functions in n-variables. 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 hypergeometric-like functions by their exponents at the divisors "at infinity" permits one to prove generalizations in n-variables of the Kummer identities for n-1 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

Cohomologie étale by Pierre Deligne( Book )

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

Modular functions of one variable, I-IV: proceedings, International Summer School, University of Antwerp, RUCA, July 17-August 3, 1972 by International Summer School on Modular Functions( )

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

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

Groupes de monodromie en géométrie algébrique [2] : Séminaire de géométrie agébrique du Bois-Marie 1967-1969. (SGA 7 II)( Book )

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

Modular Functions of One Variable II : Proceedings International Summer School University of Antwerp, RUCA July 17-August 3, 1972 by Pierre Deligne( )

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

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

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

Théorie des topos et cohomologie étale des schémas. [Séminaire de géométrie algébrique du Bois-Marie 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

Commensurabilities among Lattices in PU (1,n). (AM-132) 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 hypergeometric-like functions, that is, twists of hypergeometric functions in n-variables. 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 hypergeometric-like functions by their exponents at the divisors "at infinity" permits one to prove generalizations in n-variables of the Kummer identities for n-1 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

Monodromy of hypergeometric functions and non-lattice integral monodromy by Pierre Deligne( Book )

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

 
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Audience Level
0
Audience Level
1
  Kids General Special  
Audience level: 0.68 (from 0.53 for Commensura ... to 0.93 for Quantum fi ...)

Équations différentielles à points singuliers réguliers
Covers
Équations différentielles à points singuliers réguliersCommensurabilities among lattices in PU (1,n)Quantum fields and strings : a course for mathematiciansCohomologie étaleCohomologie étale Séminaire de géometrie algébrique du Bois Marie SGA 4 1/2Singularités irrégulières : correspondance et documentsModular functions of one variable : proceedings, international summer school, University of Antwerp, RUCA, July 17 - August 3, 1972Modular Functions of One Variable II : Proceedings International Summer School University of Antwerp, RUCA July 17-August 3, 1972Quantum fields and strings : a course for mathematicians
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
English (122)

French (83)

German (5)

Italian (1)

Dutch (1)