A $p$-adic monodromy theorem for de Rham local systems. Issue 12 (15th December 2022)

• Record Type: Journal Article
• Authors: Shimizu, Koji
• Is Part Of: Compositio mathematica. Volume 158:Issue 12(2022)
• Page Start: 2157
• Page End: 2205
• Publication Date: 2022-12-15
• Subjects: rigid analytic geometry -- p-adic Hodge theory; 14G22 -- 11F80 -- 11F85 -- 14D10 -- 14G45; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X2200776X
• Languages: English
• ISSNs: 0010-437X

Abstract

Abstract : We study horizontal semistable and horizontal de Rham representations of the absolute Galois group of a certain smooth affinoid over a $p$ -adic field. In particular, we prove that a horizontal de Rham representation becomes horizontal semistable after a finite extension of the base field. As an application, we show that every de Rham local system on a smooth rigid analytic variety becomes horizontal semistable étale locally around every classical point. We also discuss potentially crystalline loci of de Rham local systems and cohomologically potentially good reduction loci of smooth proper morphisms.