All Questions

I am very new to the world of almost mathematics and I am curious about the following: Fix an almost mathematics situation $(R,I)$ throughout. Very generally, the almost module category comes with a ...

Let $A$ be a regular factorial ring. Consider $B=A[X]/(P)$ such that $B$ is finite étale over $A$. When do we have that $B$ is also factorial?

$\DeclareMathOperator\Pic{Pic}$If $A$ is a ring, then we know that $\Pic(A)=\Pic(A_\text{red})$, but for a scheme $X$ it is false in general. On the other hand, we have that $\Pic(X)=H^{1}_{et}(X,\...

I am wondering if there is a way to describe the center of the Picard group of a non-commutative algebra. Namely, let $A$ be a finitely generated algebra over a field $k$. Denote by $\mathrm{Pic}(A)$...