Tor-dimension of $A/(a)\otimes_k B$, where $A$ and $B$ are Dedekind domains

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Let $A$ and $B$ be two Dedekind domains which contain a field $k$ which is algebraically closed in both $A$ and $B$. Let $a$ be a non zero element in $A$.

What is the Tor-dimension of $A\otimes_k B$? And of $A/(a)\otimes_k B$?