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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
10
votes
Accepted
$\mathcal{D}$-modules of level m
I find it helpful to first work through the definition of multiplication on $\mathcal{D}^{(m)}$ when $m = \infty$, in which case it reduces to the "classical" ring of differential operators in the sen …
5
votes
3
answers
1k
views
Tensor products of Weyl modules in positive characteristic
Let $G$ be a simple algebraic group over a field $k$, and let $U$ be the unipotent radical of a Borel subgroup $B$. Because $B$ normalises $U$, the group $H = B/U$ acts on the coordinate ring $\mathca …
3
votes
Accepted
Cohomology vanishing for formal completions of modules?
Yes --- this follows from EGA3 I, Chapter 0, Proposition 13.3.1 . This general result gives conditions under which it is possible to conclude that
$H^i( X, \lim\limits_\longleftarrow \mathcal{F}_k )$ …
21
votes
How to memorise (understand) Nakayama's lemma and its corollaries?
I usually find the statement of Nakayama's Lemma easy to remember because of its proof, which is really nothing more than the definition of the Jacobson radical plus the existence of maximal left idea …