Towards a non-archimedean analytic analog of the Bass-Quillen conjecture

Abstract

We suggest an analog of the Bass-Quillen conjecture for smooth affinoid algebras over a complete non-archimedean field. We prove this in the rank-1 case, i.e. for the Picard group. For complete discretely valued fields and regular affinoid algebras that admit a regular model (automatic if the residue characteristic is zero) we prove a similar statement for the Grothendieck group of vector bundles.

17 pages

References in corpus (2)

• Desingularization of quasi-excellent schemes in characteristic zero
• Algebraic K-theory and descent for blow-ups

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