La cohomologie des espaces de Lubin-Tate est libre

TL;DR

This paper proves the freeness of the a0a0l-cohomology of the Lubin-Tate tower using a global approach involving stratification of perverse sheaves and the theory of derivatives for mirabolic group representations.

Contribution

It introduces a novel global method to establish the freeness of Lubin-Tate cohomology by analyzing stratification filtrations and extension differences in perverse sheaves.

Findings

Cohomology of Lubin-Tate tower is free over a0a0l.

Stratification filtration of perverse sheaves is key to the proof.

Study of extension differences between t-structures is crucial.

Abstract

The principal result of this work is the freeness in the $ \overline{\mathbb Z}_l$-cohomology of the Lubin-Tate tower. The strategy is of global nature and relies on studying the filtration of stratification of the perverse sheaf of vanishing cycles of some Shimura varieties of Kottwitz-Harris-Taylor types, whose graduates can be explicited as some intermediate extension of some local system constructed in the book of Harris andTaylor. The crucial point relies on the study of the difference between such extension for the two classical $t$-structures $p$ and $p+$. The main ingredients use the theory of derivative for representations of the mirabolic group.