Timeline for Seminorms on tensor products of affinoid algebras
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 4, 2017 at 2:20 | comment | added | nfdc23 | Also see 7.2.6/3 in the BGR book for how the "reduction" functor $\widetilde{(\cdot)}$ interacts with the formation of certain Laurent domains, since you mention being interested in the special case that $A$ and $B$ correspond to affinoid subdomains of ${\rm{Sp}}(C)$. | |
| Sep 3, 2017 at 21:08 | comment | added | nfdc23 | This fails for $C=K$ and reduced $A$ and $B$ with $K$-finite $A$ such that $A \otimes_K B$ is non-reduced (nonzero nilpotents have $\nu_2=0$, $\nu_1\ne 0$). Sup-norm $\le 1$ is power-boundedness, so it seems relevant to note that $\widetilde{A} \otimes_{\widetilde{K}} \widetilde{B} \rightarrow (A \widehat{\otimes}_K B)^{\sim}$ is an isomorphism for algebraically closed $K$ by Satz 5 in section 6 of Bosch's Orthonormalbasen in der nichtarchimedischen Funktionentheorie in Manuscripta Math 1. Maybe that paper yields $\nu_1=\nu_2$ for $K$ algebraically closed? | |
| Sep 3, 2017 at 19:42 | review | First posts | |||
| Sep 3, 2017 at 19:51 | |||||
| Sep 3, 2017 at 19:41 | history | asked | user114125 | CC BY-SA 3.0 |