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.
Bibliographical noteFunding 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.
© 2018 London Mathematical Society
- 32C38 (primary)
ASJC Scopus subject areas
- Mathematics (all)