Fourier–Deligne transform
- Fourier–Deligne transform
-
In algebraic geometry, the Fourier–Deligne transform, or ℓ-adic Fourier transform, or geometric Fourier transform, is an operation on objects of the derived category of ℓ-adic sheaves over the affine line. It was introduced by Pierre Deligne on November 29th, 1976 in a letter to David Kazhdan as an analogue of the usual Fourier transform. It was used by Laumon (1987) to simplify Deligne's proof of the Weil conjectures.
References
- Katz, Nicholas M.; Laumon, Gérard (1985), "Transformation de Fourier et majoration de sommes exponentielles", Publications Mathématiques de l'IHÉS (62): 361–418, ISSN 1618-1913, MR823177 erratum, http://www.numdam.org/item?id=PMIHES_1985__62__145_0
- Kiehl, Reinhardt; Weissauer, Rainer (2001), Weil conjectures, perverse sheaves and l'adic Fourier transform, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, 42, Berlin, New York: Springer-Verlag, ISBN 978-3-540-41457-5, MR1855066
- Laumon, G. (1987), "Transformation de Fourier, constantes d'équations fonctionnelles et conjecture de Weil", Publications Mathématiques de l'IHÉS (65): 131–210, ISSN 1618-1913, MR908218, http://www.numdam.org/item?id=PMIHES_1987__65__131_0
Wikimedia Foundation.
2010.
Look at other dictionaries:
Fourier transform — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms The Fourier transform is a mathematical operation that decomposes a function into its constituent… … Wikipedia
Pierre Deligne — Pierre Deligne, March 2005 Born 3 October 1944 (1944 10 03 … Wikipedia
Artin-Schreier-Theorie — Die Artin Schreier Theorie gehört in der Mathematik zur Körpertheorie. Für Körper positiver Charakteristik p beschreibt sie abelsche Galois Erweiterungen vom Exponenten p und ergänzt damit die Kummer Theorie. Sie ist benannt nach Emil Artin und… … Deutsch Wikipedia
Kloosterman sum — In mathematics, a Kloosterman sum is a particular kind of exponential sum. Let a , b , m be natural numbers. Then :K(a,b;m)=sum {0leq xleq m 1, gcd(x,m)=1 } e^{2pi i (ax+bx^*)/m},Here x* is the inverse of x modulo m . They are named for the Dutch … Wikipedia
List of mathematics articles (D) — NOTOC D D distribution D module D D Agostino s K squared test D Alembert Euler condition D Alembert operator D Alembert s formula D Alembert s paradox D Alembert s principle Dagger category Dagger compact category Dagger symmetric monoidal… … Wikipedia
List of important publications in mathematics — One of the oldest surviving fragments of Euclid s Elements, found at Oxyrhynchus and dated to circa AD 100. The diagram accompanies Book II, Proposition 5.[1] This is a list of important publications in mathematics, organized by field. Some… … Wikipedia
Representation theory of finite groups — In mathematics, representation theory is a technique for analyzing abstract groups in terms of groups of linear transformations. See the article on group representations for an introduction. This article discusses the representation theory of… … Wikipedia
Riemann hypothesis — The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011 … Wikipedia
Michael Atiyah — Sir Michael Atiyah Born 22 April 1929 (1929 04 22) (age 82) … Wikipedia
Timeline of category theory and related mathematics — This is a timeline of category theory and related mathematics. By related mathematics is meant first hand * Homological algebra * Homotopical algebra * Topology using categories, especially algebraic topology * Categorical logic * Foundations of… … Wikipedia
