TY - JOUR T1 - An Euler–Poincaré bound for equicharacteristic étale sheaves JF - Algebra & Number Theory Y1 - 2010 A1 - Carl Miller AB -

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.

VL - 4 U4 - 21 - 45 UR - http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.648.3584 CP - 1 J1 - ANT ER -