An Euler–Poincaré bound for equicharacteristic étale sheaves

Miller, Carl

doi:10.2140/ant.2010.4.21

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

An Euler–Poincaré bound for equicharacteristic étale sheaves

Carl A. Miller

Vol. 4 (2010), No. 1, 21–45

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.

Keywords

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

Mathematical Subject Classification 2000

Primary: 14F20

Secondary: 13A35, 14F30

Milestones

Received: 21 March 2009

Revised: 21 October 2009

Accepted: 23 November 2009

Published: 14 January 2010

Authors

Carl A. Miller
Department of Mathematics 530 Church Street University of Michigan Ann Arbor, MI 48109 United States
http://www.umich.edu/~carlmi/

Vol. 4, No. 1, 2010