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arXiv · 1608.07446

Non-semi-stable loci in Hecke stacks and Fargues' conjecture

Ildar Gaisin·Naoki Imai
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Abstract

We show the Harris--Viehmann conjecture under some Hodge--Newton reducibility condition for a generalization of the diamond of a non-basic Rapoport--Zink space at infinite level, which appears as a cover of the non-semi-stable locus in the Hecke stack. We show also that the cohomology of the non-semi-stable locus with coefficient coming from a cuspidal Langlands parameter vanishes. As an application, we show the Hecke eigensheaf property in Fargues' conjecture for cuspidal Langlands parameters in the GL(2)-case.

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Ildar Gaisin, Naoki Imai. 2016-08-26. Non-semi-stable loci in Hecke stacks and Fargues' conjecture. https://doi.org/10.1017/s1474748025101308

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