All Questions
8 questions
30
votes
5
answers
4k
views
Deformation theory of representations of an algebraic group
For an algebraic group G and a representation V, I think it's a standard result (but I don't have a reference) that
the obstruction to deforming V as a representation of G is an element of H2(G,V&...
25
votes
4
answers
2k
views
algebraic group G vs. algebraic stack BG
I've gathered that it's "common knowledge" (at least among people who think about such things) that studying a (smooth) algebraic group G, as an algebraic group, is in some sense the same as studying ...
16
votes
1
answer
5k
views
Grothendieck-Messing theory for finite flat group schemes
Classical Grothendieck-Messing theory relates deformations of $p$-divisible groups to lifts of the Hodge filtration (if the ideal defining the nilpotent immersion is equipped with a PD-structure). If ...
- 21.3k
14
votes
1
answer
1k
views
Lie groups vs. algebraic groups and deformations
I am interested in deformations of (discrete subgroups of) Lie groups. But, as I understand it, deformation theory, as a theory, prefers to speak schemes.
At least the classical Lie groups can be ...
- 1,211
13
votes
1
answer
2k
views
What is the universal deformation of the formal additive group $\widehat{\mathbb{G}}_a$ over $\mathbb{F}_p$?
Lubin and Tate show in their paper Formal moduli for one-parameter formal Lie groups that for any formal group over a field $k$ of characteristic $p>0$ with height $h<\infty$, the functor of ...
- 6,069
5
votes
2
answers
773
views
Are linear algebraic groups rigid?
The underlying variety of a linear elgebraic group (say, over an algebraically closed field) is affine, so doesn't have nontrivial (infinitesimal) deformations. I'm curious to know whether it's ...
- 23.3k
5
votes
0
answers
424
views
Is it true that all smooth group schemes can be deformed?
Consider for instance the map $\mathbb Z/p^2 \to \mathbb Z/p$ and suppose we are given a group smooth scheme $G$ over $\mathbb Z/p$. Is it always possible to lift it to a smooth group scheme $G'$ over ...
- 7,746
2
votes
0
answers
574
views
tangent bundle of the toric variety of the wonderful compactification.
Let G be a adjoint group over $k$,algebraically closed of caracteristic zero.
Let $\overline{G}$ be its wonderful compactification.
I denote by $\overline{T}$ the closure of the torus $T$ in $\...
- 3,472