All Questions
8 questions
7
votes
2
answers
458
views
A technical question about derivations of sheaves on group schemes
Let $G$ be a group scheme (for instance, over $k$ a field of characteristic 0).
Let $e$ be its unit.
I denote by $O_G$ the structural sheaf of $G$.
Let $D_e : O_{G,e} \to k$ a derivation.
I would ...
- 1,320
6
votes
1
answer
281
views
Cokernel of map of étale sheaves
Let $p:\mathbb{G}_m\to \operatorname{Spec} k$ be the structure map, and let $T$ be an algebraic $k$-torus viewed as an étale sheaf over $k$. Why is the cokernel of the canonical map $T\to p_*p^*T$ ...
- 115
5
votes
1
answer
512
views
Do we have $\underline{\operatorname{Ext}}^i_\text{fppf}(\mathbb{G}_a,\mathbb{G}_m)=0$ for $i>0$?
Let $k$ be a characteristic zero field and consider the category $(\mathsf{Sch}/k)_\text{fppf}$ of schemes over $k$ with the fppf topology. I know that $\underline{\operatorname{Hom}}(\mathbb{G}_a,\...
- 721
5
votes
0
answers
375
views
What is an example of a cokernel $B/\phi(A)$ in group schemes which does not have $A=\mu_d$ and requires the fppf topology to be a sheaf?
Let $S$ be affine. A bit of background: Let us think of $S$-group schemes as abelian sheaves over a given site (etale, Zariski, fppf, etc). When we take a cokernel of a morphism $\phi$ this category: $...
- 3,539
2
votes
0
answers
239
views
Do we have $\underline{\operatorname{Ext}}^i_\text{fppf}(\widehat{\mathbb{G}}_a,\mathbb{G}_m)=0$ for $i>0$?
Let $k$ be a characteristic zero field and consider the category $(\mathsf{Sch}/k)_\text{fppf}$ of schemes over $k$ with the fppf topology. I know that $\underline{\operatorname{Hom}}(\mathbb{G}_a,\...
- 721
2
votes
0
answers
121
views
Norm of sections on $T$-invariant subspace of a homogenous space over $\mathbb{Q}_p$
Let $K=\mathbb{Q}_p$ and $G$ a split reductive group over $K$ with split maximal torus $T$. Furthermore, $X$ is a smooth projective variety over $K$ with a free $G$-action. Let $U \subset X$ be a $T$-...
- 473
2
votes
0
answers
167
views
Explicit construction of a presentation of a constructible sheaf of $\mathbb{Z}$-modules
This question was prompted by the two following:
Constructible étale sheaves on X are étale algebraic spaces over X
Naive question about constructing constructible sheaves
If I have a ...
- 617
2
votes
0
answers
180
views
on geometric Satake and functions
Let $G(F)/G(O)$ the affine grassmanian with $F=k((t))$ where $k$ is a finite field.
For $\lambda$ a dominant cocharacter, we have by Cartan decomposition the schubert strata $\overline{Gr^{\lambda}}$....
- 3,472