Equicharacteristic Étale Cohomology in Dimension One
نویسنده
چکیده
The Grothendieck-Ogg-Shafarevich formula expresses the Euler characteristic of an étale sheaf on a curve in terms of local data. The purpose of this paper is to prove a version of the G-O-S formula which applies to equicharacteristic sheaves (a bound, rather than an equality). This follows a proposal of R. Pink. The basis for the result is the characteristic-p “Riemann-Hilbert” correspondence, which relates equicharacteristic étale sheaves to OF,X -modules. In the paper we prove a version of this correspondence for curves, considering both local and global settings. In the process we define an invariant, the “minimal root index,” which measures the local complexity of an OF,X -module. This invariant provides the local terms for the main result.
منابع مشابه
On Some Local Cohomology Modules
All rings in this paper are commutative and Noetherian. If R is a ring and I ⊂ R is an ideal, cd(R, I) denotes the cohomological dimension of I in R, i.e. the largest integer i such that the i-th local cohomology module H i I(M) doesn’t vanish for some R-module M . For the purposes of this introduction R is a complete equicharacteristic regular local d-dimensional ring with a separably closed r...
متن کاملComparison of Motivic and simplicial operations in mod-l-motivic and étale cohomology
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تاریخ انتشار 2009