Moduli of local shtukas and Harris’s conjecture

IF 0.8 Q2 MATHEMATICS Tunisian Journal of Mathematics Pub Date : 2021-10-20 DOI:10.2140/tunis.2021.3.749
D. Hansen
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引用次数: 7

Abstract

We prove, under a certain assumption of “Hodge-Newton reducibility”, a strong form of a conjecture of Harris on the cohomology of moduli spaces of mixed-characteristic local shtukas for GLn. Our strategy is roughly based on a previous strategy developed by Mantovan in the setting of p-divisible groups, but the arguments are completely different. In particular, we reinterpret and generalize the Hodge-Newton filtration of a p-divisible group in terms of modified vector bundles on the Fargues-Fontaine curve. We also compute the dualizing complex and compactly supported étale cohomology of any positive Banach-Colmez space over any base; this should be of independent interest.
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局部shtukas模与Harri猜想
在“Hodge-Newton可约性”的一定假设下,我们证明了Harris关于GLn的混合特征局部shtukas模空间的上同调猜想的一个强形式。我们的策略大致基于Mantovan之前在p-可分群的设置中开发的策略,但论点完全不同。特别地,我们用Fargues-Fontaine曲线上的修正向量丛重新解释和推广了p-可分群的Hodge-Newton滤。我们还计算了任意基上任意正Banach Colmez空间的对偶复紧支撑étale上同调;这应该是独立的利益。
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来源期刊
Tunisian Journal of Mathematics
Tunisian Journal of Mathematics Mathematics-Mathematics (all)
CiteScore
1.70
自引率
0.00%
发文量
12
期刊最新文献
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