Maximal varieties and the local Langlands correspondence for GL(n)

Details Maximal varieties and the local Langlands correspondence for GL(n) Maximal varieties and the local Langlands correspondence for GL(n)

2011-09-16

arxiv.org/abs/1109.3522v2

Mathematics

Number Theory

59 pages

Scientific paper

In the second author's study of deformation spaces of formal modules, there arose a certain variety X, defined over a finite field, which was conjectured to have the property of "maximality": the number of rational points of X is the largest possible among varieties with the same Betti numbers as X. In the current paper we prove this conjecture, and indeed give a complete description of the zeta function of X. The variety X is derived from a certain unipotent algebraic group, in an analogous manner as Deligne-Lusztig varieties are derived from reductive algebraic groups. As a consequence, the cohomology of X can be shown to realize a piece of the local Langlands correspondence for certain wild Weil parameters of low conductor.

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