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Reinhardt Kiehl

Other affiliations: University of Münster
Bio: Reinhardt Kiehl is an academic researcher from University of Mannheim. The author has contributed to research in topics: Conjecture & Étale cohomology. The author has an hindex of 12, co-authored 17 publications receiving 1038 citations. Previous affiliations of Reinhardt Kiehl include University of Münster.

Papers
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Book
10 Feb 1988
TL;DR: In this article, Deligne's Proof of the Weil Conjecture is used to prove the rationality of Weil's Weil conjecture, based on the notion of the fundamental group.
Abstract: I The Essentials of Etale Cohomology Theory- II Rationality of Weil ?-Functions- III The Monodromy Theory of Lefschetz Pencils- IV Deligne's Proof of the Weil Conjecture- Appendices- A I The Fundamental Group- A II Derived Categories- A III Descent

249 citations

Book
19 Oct 2010
TL;DR: In this article, the General Weil Conjectures (Deligne's Theory of Weights) are used to prove the Finiteness Theorem for Etale Sheaves, along with the Lefschetz Theory and Brylinski-Radon Transform.
Abstract: I. The General Weil Conjectures (Deligne's Theory of Weights).- II. The Formalism of Derived Categories.- III. Perverse Sheaves.- IV. Lefschetz Theory and the Brylinski-Radon Transform.- V. Trigonometric Sums.- VI. The Springer Representations.- B. Bertini Theorem for Etale Sheaves.- C. Kummer Extensions.- D. Finiteness Theorems.

153 citations


Cited by
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Book
01 Jan 2009
TL;DR: In this paper, a general introduction to higher category theory using the formalism of "quasicategories" or "weak Kan complexes" is provided, and a few applications to classical topology are included.
Abstract: This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to the study of higher versions of Grothendieck topoi. A few applications to classical topology are included.

1,879 citations

Journal ArticleDOI
TL;DR: It follows almost as imme- diately, by "smashing" arguments, that the adjoint is given by tensor product with a dualising complex as mentioned in this paper, which is an immediate consequence of Brown's representability theorem.
Abstract: Grothendieck proved that if f: X ) Y is a proper morphism of nice schemes, then Rf* has a right adjoint, which is given as tensor product with the relative canonical bundle. The original proof was by patching local data. Deligne proved the existence of the adjoint by a global argument, and Verdier showed that this global adjoint may be computed locally. In this article we show that the existence of the adjoint is an immediate consequence of Brown's representability theorem. lIt follows almost as imme- diately, by "smashing" arguments, that the adjoint is given by tensor product with a dualising complex. Verdier's base change theorem is an easy conse- quence. DEPARTMENT OF MATHEMATICS, UNIVERSITY OF VIRGINIA, CHARLOTTESVILLE, VIRGINIA 22903 E-mail address: an3rQvirginia. edu This content downloaded from 157.55.39.27 on Wed, 07 Sep 2016 06:26:19 UTC All use subject to http://about.jstor.org/terms

689 citations

Journal ArticleDOI
Morihiko Saito1
TL;DR: In this paper, the notion of complexe pur and faisceaux pervers purs has been investigated in the context of modules filtrés holonomes, a notion of which was introduced by Deligne and Gabber.
Abstract: Dans [7], Deligne a introduit la notion de complexe pur, et démontré la stabilité par image directe par morphismes propres (i.e. la version relative de la conjecture de Weil). Cette théorie, combinée avec celle de faisceaux pervers, a été ensuite développée par Beilinson-Bernstein-Deligne-Gabber[l]: ils ont démontré le théorème de décomposition, et la stabilité des faisceaux pervers purs par images directes intermédiaires (en particulier, la pureté des complexes d'intersection) [loc. cit]. D'après la philosophie de Deligne [6, 7], on a conjecturé qu'il existerait des objets en car. 0, correspondant aux complexes purs, cf. [2,3,4] etc. Le but de cet article est de donner une réponse positive: en utilisant la théorie de £)-Modules filtrés, la théorie de la filtration V [17, 22] et la théorie de faisceaux pervers, on définit la notion de Module de Hodge polarisable (cf. 5.1-2), qui doit correspondre à celle de faisceau pervers pur, et on démontre la stabilité par images directes (perverses) par un morphisme projectif avec un théorème de Lefschetz fort relatif et une polarisation induite sur les parties primitives (i.e. une théorie de Hodge-Lefschetz relative), cf. 5.3.1. Soient X une variété analytique complexe lisse, 3)x le faisceau des opérateurs différentiels analytiques muni de la filtration F par degré d'opérateur, et MF(â)x} la catégorie des .^-Modules filtrés. On dit que (M, F)^MF(3)X} est holonome, si M est un .â^-Module holonome [16, 18] et GrM est un Gr£Dx-ModulQ cohérent (i.e. F est une bonne filtration de M[loc. cit]). Soit MFh(3)x} la sous-catégorie pleine de MF(3)X) des .â^-Modules filtrés holonomes. D'après Kashiwara [16] on a le foncteur

665 citations

Book ChapterDOI
01 Jan 1989
TL;DR: In this article, Grothendieck described the complete profini of the groupe fondamental de X := P1(C) − {0,1, oo}, avec son action de Gal(\(\overline Q \)/ℚ) est un oject remarquable, and qu’il faudrait l'etudier.
Abstract: Le present article doit beaucoup a A. Grothendieck. Il a invente la philosophie des motifs, qui est notre fil directeur. Il y a quelques cinq ans, il m’a aussi dit, avec force, que le complete profini \({\hat \pi _1}\) du groupe fondamental de X := P1(C) — {0,1, oo} , avec son action de Gal(\(\overline Q \)/ℚ) est un oject remarquable, et qu’il faudrait l’etudier.

557 citations