nLab
Weil cohomology theory

Contents

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

(,1)(\infty,1)-Topos Theory

(∞,1)-topos theory

Background

Definitions

Characterization

Morphisms

Extra stuff, structure and property

Models

Constructions

structures in a cohesive (∞,1)-topos

Contents

Idea

A Weil cohomology theory is defined to be a cohomology theory on a suitable class of projective varieties which satisfies some natural set of axioms among which is notably Poincaré duality and the existence of a Lefschetz fixed point theorem.

These axioms are named after André Weil, who noticed that the existence of such a cohomology theory would already imply the Weil conjectures about the behaviour of the number of points in algebraic varieties.

Examples of Weil cohomology theories, hence of cohomology theories satisfying these axioms, are the variants of étale cohomology known as l-adic cohomology or better pro-étale cohomology.

References

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Last revised on July 14, 2014 at 04:45:33. See the history of this page for a list of all contributions to it.