Pierre Deligne

Pierre René, Viscount Deligne (French: [dəliɲ]; born 3 October 1944) is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Prize, and 1978 Fields Medal.

Early life and education

Deligne was born in

From 1970 until 1984, Deligne was a permanent member of the IHÉS staff. During this time he did much important work outside of his work on algebraic geometry. In joint work with George Lusztig, Deligne applied étale cohomology to construct representations of finite groups of Lie type; with Michael Rapoport, Deligne worked on the moduli spaces from the 'fine' arithmetic point of view, with application to modular forms. He received a Fields Medal in 1978. In 1984, Deligne moved to the Institute for Advanced Study in Princeton.

Hodge cycles

In terms of the completion of some of the underlying Grothendieck program of research, he defined

He was awarded the Fields Medal in 1978, the Crafoord Prize in 1988, the Balzan Prize in 2004, the Wolf Prize in 2008, and the Abel Prize in 2013, "for seminal contributions to algebraic geometry and for their transformative impact on number theory, representation theory, and related fields". He was elected a foreign member of the Academie des Sciences de Paris in 1978.

In 2006 he was ennobled by the Belgian king as viscount.^[3]

In 2009, Deligne was elected a foreign member of the Royal Swedish Academy of Sciences^[4] and a residential member of the American Philosophical Society.^[5] He is a member of the Norwegian Academy of Science and Letters.^[6]

Selected publications

• Deligne, Pierre (1974). "La conjecture de Weil: I". Publications Mathématiques de l'IHÉS. 43: 273–307.
  S2CID 123139343
  .
• Deligne, Pierre (1980). "La conjecture de Weil : II". Publications Mathématiques de l'IHÉS. 52: 137–252.
  S2CID 189769469
  .
• Deligne, Pierre (1990). "Catégories tannakiennes". Grothendieck Festschrift Vol II. Progress in Mathematics. 87: 111–195.
• Deligne, Pierre;
  S2CID 1357812
  .
• Deligne, Pierre;
  ISBN 0-691-00096-4
  .
• Quantum fields and strings: a course for mathematicians. Vols. 1, 2. Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study, Princeton, NJ, 1996–1997. Edited by Pierre Deligne,
  ISBN 0-8218-1198-3
  .

• "Deligne's letter to Piatetskii-Shapiro (1973)" (PDF). Archived from the original (PDF) on 7 December 2012. Retrieved 15 December 2012.
• "Deligne's letter to Jean-Pierre Serre (around 1974)". 15 December 2012.
• "Deligne's letter to Looijenga (1974)" (PDF). Retrieved 20 January 2020.
• "Deligne's letter to Millson (1986)" (PDF). Retrieved 11 November 2021.

Concepts named after Deligne

The following mathematical concepts are named after Deligne:

• Brylinski-Deligne extensions
• Deligne torus
• Deligne–Lusztig theory
• Deligne–Mumford moduli space of curves
• Deligne–Mumford stacks
• Fourier–Deligne transform
• Deligne cohomology
• Deligne motive^[7]
• Deligne tensor product of abelian categories (denoted ${\displaystyle \boxtimes }$)^[8]
• Deligne's theorem
• Langlands–Deligne local constant
• Weil-Deligne group

Additionally, many different conjectures in mathematics have been called the Deligne conjecture:

• Deligne's conjecture on Hochschild cohomology.
• The
  Deligne conjecture on special values of L-functions is a formulation of the hope for algebraicity of L(n) where L is an L-function
  and n is an integer in some set depending on L.
• There is a Deligne conjecture on 1-motives arising in the theory of motives in algebraic geometry.
• There is a Gross–Deligne conjecture in the theory of complex multiplication.
• There is a Deligne conjecture on monodromy, also known as the weight monodromy conjecture, or purity conjecture for the monodromy filtration.
• There is a
  exceptional Lie groups
  .
• There is a conjecture named the Deligne–Grothendieck conjecture for the discrete Riemann–Roch theorem in characteristic 0.
• There is a conjecture named the Deligne–Milnor conjecture for the differential interpretation of a formula of Milnor for Milnor fibres, as part of the extension of nearby cycles and their Euler numbers.
• The Deligne–Milne conjecture is formulated as part of motives and Tannakian categories.
• There is a Deligne–Langlands conjecture of historical importance in relation with the development of the
  Langlands philosophy
  .
• Deligne's conjecture on the Lefschetz trace formula^[9] (now called Fujiwara's theorem for equivariant correspondences).^[10]

See also

• Brumer–Stark conjecture
• E7½
• Hodge–de Rham spectral sequence
• Logarithmic form
• Kodaira vanishing theorem
• Moduli of algebraic curves
• Motive (algebraic geometry)
• Perverse sheaf
• Riemann–Hilbert correspondence
• Serre's modularity conjecture
• Standard conjectures on algebraic cycles

References

1. JSTOR 40068158
   . Retrieved 13 January 2024.
2. ISSN 0273-0979
   .
3. ^ Official announcement ennoblement – Belgian Federal Public Service. 18 July 2006 Archived 30 October 2007 at the Wayback Machine
4. ^ Royal Swedish Academy of Sciences: Many new members elected to the Academy, press release on 12 February 2009 Archived 10 July 2018 at the Wayback Machine
5. ^ "APS Member History". search.amphilsoc.org. Retrieved 23 April 2021.
6. ^ "Gruppe 1: Matematiske fag" (in Norwegian). Norwegian Academy of Science and Letters. Retrieved 2 August 2022.
7. ^ motive in nLab
8. ^ Deligne tensor product of abelian categories in nLab
9. ^ Yakov Varshavsky (2005), "A proof of a generalization of Deligne's conjecture", p. 1.
10. ^ Martin Olsson, "Fujiwara's Theorem for Equivariant Correspondences", p. 1.

External links

Wikiquote has quotations related to Pierre Deligne.

Wikinews has related news:

• Norwegian Academy of Science and Letters awards Belgian mathematician Pierre Deligne with Abel prize of 2013

• O'Connor, John J.; Robertson, Edmund F., "Pierre Deligne", MacTutor History of Mathematics Archive, University of St Andrews
• Pierre Deligne at the Mathematics Genealogy Project
• Roberts, Siobhan (19 June 2012). "Simons Foundation: Pierre Deligne". Simons Foundation. – Biography and extended video interview.
• Pierre Deligne's home page at Institute for Advanced Study
• ISBN 951-410-352-1, archived from the original (PDF) on 12 July 2012{{citation}}: CS1 maint: location missing publisher (link
  ) An introduction to his work at the time of his Fields medal award.