All Questions
8 questions
3
votes
0
answers
171
views
Grothendieck-Messing in characteristic 0?
Let $A$ is an abelian scheme over a base scheme $S$. Let $S \rightarrow S'$ be a thickening defined by an ideal of square zero (for example).
If $p$ is locally nilpotent on $S$, then Serre-Tate and ...
- 261
6
votes
1
answer
373
views
For an abelian scheme, $R^pf_* \Omega^q$ is locally free and its formation is compatible with any base change
Let $k$ be a field, $\bar{R} \to R$ a local homomorphism of artinian local rings with the residue fields $k$, $I$ its kernel, $A/R$ an abelian scheme, and $\mathscr{T}$ its tangent sheaf.
Let $A_0 = A ...
- 1,144
2
votes
1
answer
202
views
Identification of cohomology sheaf in the definition of the Kodaira-Spencer morphism for abelian schemes
Let $p:A \to S$ be a projective abelian scheme, where $S$ is some smooth scheme over a base field $k$. Then we have the Kodaira-Spencer morphism
$$
\kappa : T_{S/k} \to R^1p_*T_{A/S}
$$
where $T_{S/k}$...
- 16.1k
0
votes
1
answer
354
views
Reference for Hodge loci on moduli space of principally polarised abelian varieties
Can someone suggest a reference to study Hodge locus, period mappings and period domains on moduli space of principally polarised abelian varieties?
More precisely, consider the moduli space of ...
- 474
11
votes
0
answers
310
views
Surfaces with $q=2$ and generically finite Albanese map
I have a family of surfaces of general type $S$ with $q(S)=2$, and such that the Albanese map $$\alpha \colon S \longrightarrow A:=\mathrm{Alb}(S)$$ is generically finite of degree $n$. By a result of ...
- 66.3k
4
votes
0
answers
245
views
Deformations of the moduli space of ppav's
Consider the complex algebraic moduli space $X:=\mathcal A_g^n$ of ppav's of dimension $g$ with some high enough level $n$ structure (so that it represents the corresponding functor).
Can one compute ...
- 193
4
votes
1
answer
795
views
Deformation space of non-ordinary abelian varieties
It is a well known result of Serre and Tate that if $A$ is an ordinary abelian variety over a field $k$ of characteristic $p>0$, then the deformation space $\mathcal{M}$ of $A$ to an abelian ...
- 186
3
votes
0
answers
935
views
Grothendieck-Messing theory
Hello,
I would like to work out some examples of deformation of isogenies via Grothendieck-Messing theory. Let's take an easy example: Let A be an abelian variety over $k=\overline{\mathbb{F}_p}$ and ...
- 31