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2010 An Euler–Poincaré bound for equicharacteristic étale sheaves
Carl Miller
Algebra Number Theory 4(1): 21-45 (2010). DOI: 10.2140/ant.2010.4.21

Abstract

The Grothendieck–Ogg–Shafarevich formula expresses the Euler characteristic of an étale sheaf on a characteristic-p curve in terms of local data. The purpose of this paper is to prove an equicharacteristic version of this formula (a bound, rather than an equality). This follows work of R. Pink.

The basis for the proof of this result is the characteristic-p Riemann–Hilbert correspondence, which is a functorial relationship between two different types of sheaves on a characteristic-p scheme. In the paper we prove a one-dimensional version of this correspondence, considering both local and global settings.

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Carl Miller. "An Euler–Poincaré bound for equicharacteristic étale sheaves." Algebra Number Theory 4 (1) 21 - 45, 2010. https://doi.org/10.2140/ant.2010.4.21

Information

Received: 21 March 2009; Revised: 21 October 2009; Accepted: 23 November 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1185.14016
MathSciNet: MR2592012
Digital Object Identifier: 10.2140/ant.2010.4.21

Subjects:
Primary: 14F20
Secondary: 13A35 , 14F30

Keywords: characteristic-$p$ curves , étale sheaves , Frobenius endomorphism , Grothendieck–Ogg–Shafarevich formula , minimal roots , Riemann–Hilbert correspondence

Rights: Copyright © 2010 Mathematical Sciences Publishers

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