All Questions

Let $f : X \to Y$ be a morphism between two Noetherian schemes. Then $f_*$(respect to $R^1f_*$) sends coherent sheaves to coherent sheaves if and only if $f$ is universally closed (respect to ...

I am considering the following correspondence: Let $X$ be quasi compact quasi separated schemes.Consider a pseudo functor \begin{equation}Sch\rightarrow CAT :U\mapsto Qcoh(U),f:U\rightarrow V\mapsto f^...

The other direction is well known. I think it is true and I was told by several other guys doing algebraic geometry that it is indeed true but they did not know how to prove. I am also wondering ...

I came across the following Lemma in Mitsuyasu Hashimoto's Equivariant Twisted Inverses; it is Lemma 11.2 on page 107 of this pdf. Let $\mathcal{A}$ be an abelian category which satisfies the (AB3) ...

The proof of statements either uses Galois theory or Artin primitive element theorem.I would like to know whether there is a proof without using these.The reason to avoid using Galois theory is that ...