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arXiv · 1611.02082

Mirabolic group, ramified Newton stratification and cohomology of Lubin-Tate spaces

Pascal Boyer
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Abstract

In my 2009 paper at Inventiones, we determine the cohomology of Lubin-Tate spaces globally using the comparison theorem of Berkovich by computing the fibers at supersingular points of the perverse sheaf of vanishing cycle $\Psi$ of some Shimura variety of Kottwitz-Harris-Taylor type. The most difficult argument deals with the control of maps of the spectral sequences computing the sheaf cohomology of both Harris-Taylor perverse sheaves and those of $\Psi$. In this paper, we bypass these difficulties using the classical theory of representations of the mirabolic group and a simple geometric argument.

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Pascal Boyer. 2016-11-07. Mirabolic group, ramified Newton stratification and cohomology of Lubin-Tate spaces. https://doi.org/10.24033/bsmf.2797

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