I am trying to read myself about Picard group. This is really interesting for me. A Prüfer domain $R$ is a Bézout domain iff Picard group of $R$ is zero. Is there some good properties of Picard group ...
Is it true that for any (commutative, unital) ring $A$ that $A[s,t], A[x^2, xy, y^2]$ cannot be isomorphic as rings? This is mentioned in passing in Eisenbud-Harris, Geometry of Schemes Exercise ...
Excerpt from Waterhouse, 14.4 Structure of Finite Connected groups. Thm. Let $A$ represent a finite connected group scheme over a perfect field of characteristic $p$. Then $A$ has the form $k[X_1, ...