The Derived l-modular Unipotent Block of p-adic GLnOberseminar Darstellungstheorie
by
Endenicher Allee 60/1.008 - Seminarraum
Mathezentrum
The theory of smooth representations of reductive groups over
p-adic fields appears on one side of the local Langlands correspondence,
which relates it to representations associated to the absolute Galois
group of the p-adic field. With coefficients in the complex numbers, the
decomposition of Bernstein describes the blocks of the category of
representations, and in many cases the theory of types gives an
equivalence between each block and the category of modules over an
explicit Hecke algebra. When we generalise the coefficients to
algebraically closed fields of characteristic l not equal to p, all of
this can fail. Bernstein's decomposition fails for most groups, though
it still holds for GLn. However, even in this case, the equivalence with
a Hecke algebra fails, though partial results are still known, involving
instead a Schur algebra. Building on these, I give an equivalence
between a derived category of the unipotent block (the block containing
the trivial representation) and perfect complexes over a dg-enriched
Schur algebra.