Nonstandard Étale Cohomology
نویسندگان
چکیده
A lot of good properties of étale cohomology only hold for torsion coefficients. We use “enlargement of categories” as developed in [BS] to define a cohomology theory that inherits the important properties of étale cohomology while allowing greater flexibility with the coefficients. In particular, choosing coefficients Z/P Z (for P an infinite prime and Z the enlargement of Z) gives a Weil cohomology, and choosing ∗Z/lh∗Z (for l a finite prime and h an infinite number) allows comparison with ordinary l-adic cohomology. More generally, for every N ∈ Z, we get a category of Z/NZ–constructible sheaves with good properties.
منابع مشابه
Comparison of Motivic and simplicial operations in mod-l-motivic and étale cohomology
In this paper we explore the relationships between the motivic and simplicial cohomology operations defined on mod-l motivic cohomology. We also explore similar relationships in étale cohomology and conclude by considering certain operations that commute with proper push-forwards.
متن کاملNotes on Étale Cohomology
These notes outline the “fundamental theorems” of étale cohomology, following [4, Ch. vi], as well as briefly discuss the Weil conjectures.
متن کامل