Sur la p-dimension des corps
Algebraic Geometry
2015-05-13 v1 Number Theory
Abstract
Let A be an excellent integral henselian local noetherian ring, k its residue field of characteristic p>0 and K its fraction field. Using an algebraization technique introduced by the first named author, and the one-dimension case already proved by Kazuya KATO, we prove the following formula: cd_p(K) = dim(A) + p-rank(k), if k is separably closed and K of characteristic zero. A similar statement is valid without those assumptions on k and K.
Keywords
Cite
@article{arxiv.0706.0671,
title = {Sur la p-dimension des corps},
author = {Ofer Gabber and Fabrice Orgogozo},
journal= {arXiv preprint arXiv:0706.0671},
year = {2015}
}