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arXiv · 0906.4093

Equicharacteristic etale cohomology in dimension one

Carl A. Miller
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Abstract

The Grothendieck-Ogg-Shafarevich formula expresses the Euler characteristic of an etale 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 etale sheaves to O_{F, 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 O_{F, X}-module. This invariant provides the local terms for the main result.

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Carl A. Miller. 2009-06-22. Equicharacteristic etale cohomology in dimension one. https://arxiv.org/abs/0906.4093

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