# Support of Tor over affinoid algebras

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.

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