Bounded linear endomorphisms of rigid analytic functions

Konstantin Ardakov; Oren Ben-Bassat

doi:10.1112/plms.12142

Bounded linear endomorphisms of rigid analytic functions

Konstantin Ardakov, Oren Ben-Bassat

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let K be a field of characteristic zero complete with respect to a non-trivial, non-Archimedean valuation. We relate the sheaf D of infinite order differential operators on smooth rigid K-analytic spaces to the algebra E of bounded K -linear endomorphisms of the structure sheaf. In the case of complex manifolds, Ishimura proved that the analogous sheaves are isomorphic. In the rigid analytic situation, we prove that the natural map D-> E is an isomorphism if and only if the ground field K is algebraically closed and its residue field is uncountable.

Original language	English
Pages (from-to)	881-900
Number of pages	20
Journal	Proceedings of the London Mathematical Society
Volume	117
Issue number	5
DOIs	https://doi.org/10.1112/plms.12142
State	Published - Nov 2018

Bibliographical note

Funding Information:
Received 25 July 2017; revised 19 February 2018; published online 16 April 2018. 2010 Mathematics Subject Classification 14G22, 32C38 (primary). The first author was supported by EPSRC grant EP/L005190/1.

Publisher Copyright:
© 2018 London Mathematical Society

Keywords

14G22
32C38 (primary)

ASJC Scopus subject areas

Mathematics (all)

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10.1112/plms.12142

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Bounded linear endomorphisms of rigid analytic functions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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