Abstract
dc:description.abstractFollowing the notion of $p$-adic analytic differential operators introduced by Ardakov--Wadsley, we establish a number of properties for coadmissible $\wideparen{\mathcal{D}}$-modules on rigid analytic spaces. Our main result is a $\wideparen{\mathcal{D}}$-module analogue of Kiehl's Proper Mapping Theorem, considering the 'naive' pushforward from \wideparen{\mathcal{D}}X-modules to f*\wideparen{\mathcal{D}}X-modules for proper morphisms $f: X\to Y$. Under assumptions which can be naturally interpreted as a certain properness condition on the cotangent bundle, we show that any coadmissible \wideparen{\mathcal{D}}X-module has coadmissible higher direct images. This implies among other things a purely geometric justification of the fact that the global sections functor in the rigid analytic Beilinson--Bernstein correspondence preserves coadmissibility, and we are able to extend this result to arbitrary twisted $\wideparen{\mathcal{D}}$-modules on analytified partial flag varieties. Our results rely heavily on the study of completed tensor products for $p$-adic Banach modules, for which we provide several new exactness criteria. We also show that the main results of Ardakov--Wadsley on the algebraic structure of $\wideparen{\mathcal{D}}$ still hold without assuming the existence of a smooth Lie lattice. For instance, we prove that the global sections \wideparen{\mathcal{D}}X(X) form a Frechet--Stein algebra for any smooth affinoid $X$.
Degree
thesis:*- Name dc:type.qualificationname
- Doctor of Philosophy (PhD)
- Level dc:type.qualificationlevel
- Doctoral
- Grantor dc:publisher.institution
- University of Cambridge
- Year dc:date.issued
- 2018
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Bode, Andreas
- Advisor dc:contributor.advisor
-
- Wadsley, Simon James
Subjects
dc:subject × 3Rights
dc:rightsIdentifiers
dc:identifier.*- Author Identifier
- 0000-0002-6043-5511
- OAI identifier oai:identifier
- oai:www.repository.cam.ac.uk:1810/277510