# Tagged Questions

**3**

votes

**0**answers

112 views

### Are there any useful Grothendieck topologies for which the H1 of $GL_n$ is not the set of rank $n$ vector bundles

Let n be a positive integer and X a scheme. Then for all the Grothendieck topologies I know (Zariski, etale, fppf) the set $H^1(X,GL_n)$ is the set of (isomorphism classes of) rank $n$ vector bundles.
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**2**

votes

**0**answers

326 views

### cohomology of projective limit of schemes

Hello,
Suppose that $X_i$ is a projective system of schemes and $F_i$ is a compatible
projective system of abelian sheaves on the $X_i$ (i.e. if $p_{ij} : X_i \to X_j$ is the
transition map, then we ...

**3**

votes

**1**answer

473 views

### How to compute cohomology groups of a closed subscheme Z of projective space, defined by a homogeneous polynomial of degree d?

Let $Z = \mathrm{Proj}\,k[x_{0},x_{1},\ldots,x_{r}]/f$ be a closed subscheme of degree $d$, i.e., $f$ is a homogeneous polynomial of degree $d$, and ...