Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Suppose $k$ is a complete nonarchimedian field, $A$ is a $k$-affinoid algebra, and $M$ is a finitely presented $A$-module. Is the set

$\tau(M)= \left\{ x \in \mathrm{Sp}(A)\,\mathrm{with}\,\mathrm{Tor}^{A}_{1}(A/\mathfrak{m}_x,M)\neq0 \right\}$

a closed analytic subset of $\mathrm{Sp}(A)$? The answer is "yes" when $A$ is regular.

share|improve this question

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.