Deformation spaces of one-dimensional formal modules and their cohomology

By M. Strauch. 2006

63 citations recorded by the source corpus.

Abstract Let M m be the formal scheme which represents the functor of deformations of a one-dimensional formal module over F ¯ p equipped with a level-m-structure. By work of Boyer (in equal characteristic) and Harris and Taylor, the l-adic etale cohomology of the generic fibre M m of M m realizes simultaneously the local Langlands and Jacquet–Langlands correspondences. The proofs given so far use Drinfeld modular varieties or Shimura varieties to derive this local result. In this paper we show without the use of global moduli spaces that the Jacquet–Langlands correspondence is realized by the Euler–Poincare characteristic of the cohomology. Under a certain finiteness assumption on the cohomology groups, it is shown that the correspondence is realized in only one degree. One main ingredient of the proof consists in analyzing the boundary of the deformation spaces and in studying larger spaces which can be considered as compactifications of the spaces M m .

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3a8123db0cd5757c6ccfc74ee93da8fa62f8741e

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Towards a theory of local Shimura varieties (2014, background): “(ii) There is a series of papers by Mieda [70, 71, 72] in which he transposes the method of Strauch to the case when G = GSp4.”