Journal ArticleDOI
La conjecture de Weil I.
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In this article, the authors implique l'accord avec les conditions generales d'utilisation (http://www.numdam.org/legal.php).Abstract:
© Publications mathematiques de l’I.H.E.S., 1974, tous droits reserves. L’acces aux archives de la revue « Publications mathematiques de l’I.H.E.S. » (http://www. ihes.fr/IHES/Publications/Publications.html), implique l’accord avec les conditions generales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systematique est constitutive d’une infraction penale. Toute copie ou impression de ce fichier doit contenir la presente mention de copyright.read more
Citations
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Journal ArticleDOI
Koszul Duality Patterns in Representation Theory
TL;DR: In this paper, Soergel et al. showed that the block of the Bernstein-Gelfand-gelfand category O that corresponds to any fixed central character is a Koszul ring and the dual of that ring governs a certain subcategory of the category O again.
Journal ArticleDOI
Real Homotopy Theory of Kähler Manifolds.
TL;DR: In this paper, the De Rham Complex of a Compact K~ihler Manifold has been shown to be a homotopy theory of differential algebras.
Book
Random matrices, Frobenius eigenvalues, and monodromy
Nicholas M. Katz,Peter Sarnak +1 more
TL;DR: In this paper, the main results of the main theorem were reformulated and reduction steps in proving the main theorems were taken in the following order: Test functions Haar measure Tail estimates Large $N$ limits and Fredholm determinants Several variables Equidistribution Monodromy of families of curves Monodromes of some other families GUE discrepancies in various families Distribution of low-lying Frobenius eigenvalues in different families Appendix AD: Densities Appendix AG: Graphs References.
Journal ArticleDOI
Equivariant cohomology, Koszul duality, and the localization theorem
TL;DR: In this paper, the authors considered the action of a compact Lie group K on a space X and gave a description of equivariant homology and intersection homology in terms of Equivariant geometric cycles.
Journal ArticleDOI
Smoothness, semi-stability and alterations
TL;DR: In this article, the authors present conditions générales d'utilisation (http://www.numdam.org/conditions), i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
References
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Journal ArticleDOI
Real Homotopy Theory of Kähler Manifolds.
TL;DR: In this paper, the De Rham Complex of a Compact K~ihler Manifold has been shown to be a homotopy theory of differential algebras.
Journal ArticleDOI
Numbers of solutions of equations in finite fields
TL;DR: In this paper, it was shown that for a prime of the form p = 4n + 1, the number of solutions of any congruence ax − by ≡ 1 (mod p) for a given biquadratic character of 2 mod p can be computed using Gaussian sums of order 3.
Book ChapterDOI
Les Constantes des Equations Fonctionnelles des Fonctions L
TL;DR: In this article, a demonstration simple du theoreme de Langlands [9] (deja prouve au signe pres par Dwork [6]) is presented, which permet d'ecrire la constante des equations fonctionnelles des fonctions L d’Artin (ou de Weil [19]) comme produit de constantes locales.
Journal ArticleDOI
Contributions to the theory of Ramanujan's function τ(n) and similar arithmetical functions: II. The order of the Fourier coefficients of integral modular forms
TL;DR: In this article, the authors consider an integral modular form of dimensions −κ, where κ > 0, and Stufe N which vanishes at all rational cusps of the fundamental region.