Bounded linear endomorphisms of rigid analytic functions

Konstantin Ardakov, Oren Ben-Bassat

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)881-900
Number of pages20
JournalProceedings of the London Mathematical Society
Issue number5
StatePublished - 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


  • 14G22
  • 32C38 (primary)

ASJC Scopus subject areas

  • Mathematics (all)


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