Incarnations of Berthelot's conjecture

JOURNAL OF NUMBER THEORY

卷:166

Article

Lazda, Christopher¹ 

[1] Univ Padua, Dipartimento Matemat Pura & Applicata, Via Trieste 63, I-35121 Padua, Italy

关键词: Berthelot's conjecture;    Arithmetic D-modules;    Overconvergent F-isocrystals;    p-Adic cohomology;   

DOI  :  10.1016/j.jnt.2016.02.028

来源: Elsevier

【 摘 要 】

In this article we give a survey of the various forms of Berthelot's conjecture and some of the implications between them. By proving some comparison results between push-forwards of overconvergent isocrystals and those of arithmetic D-modules, we manage to deduce some cases of the conjecture from Caro's results on the stability of overcoherence under push-forward via a smooth and proper morphism of varieties. In particular, we show that Ogus' convergent push-forward of an overconvergent F-isocrystal under a smooth and projective morphism is overconvergent. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free