A simpson correspondence in positive characteristic

Abstract

Let p be a prime number, k a perfect field of characteristic p > 0, X a smooth k-scheme and DX(m) the algebra of (arithmetic) differential operators of level m ≥ 0. We study the Azumaya nature of this algebra and show how to construct, using an additional data, a splitting of a completion (along some ideal contained in its center) of it. © 2010 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.