07538nas a2200145 4500008004100000022001400041245006900055210006600124260001500190300001200205490000600217520708300223100001707306856006907323 2010 eng d a1937-065200aAn Euler–Poincaré bound for equicharacteristic étale sheaves0 aEuler–Poincaré bound for equicharacteristic étale sheaves c2010/01/14 a21 - 450 v43 a
The Grothendieck–Ogg–Shafarevich formula expresses the Euler characteristic of an étale sheaf on a characteristic- 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- Riemann–Hilbert correspondence, which is a functorial relationship between two different types of sheaves on a characteristic- scheme. In the paper we prove a one-dimensional version of this correspondence, considering both local and global settings.
1 aMiller, Carl uhttp://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.648.3584