A cohomological approach to Serre's Minkowski-style bounds
Giovanni Di Matteo (`06)
Ecole Normale Superieure de Lyon (forthcoming)
In recent years, Serre has adapted a classical theorem of Minkowski
to give bounds for the ℓ-valuation of |G(k)|, where G is a
reductive group or semi-simple of inner type. It was observed by Serre
that these bounds may be recovered from ℓ-adic cohomology. We
illuminate the cohomological approach in the case of G = GLn.