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

Publisher Copyright:
© 2018 London Mathematical Society


  • 14G22
  • 32C38 (primary)

ASJC Scopus subject areas

  • General Mathematics


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