Motivic integration on the Hitchin fibration

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-12-25 DOI:10.14231/ag-2021-004

F. Loeser, Dimitri Wyss

引用次数: 8

Abstract

We prove that the moduli spaces of twisted $\mathrm{SL}_n$ and $\mathrm{PGL}_n$-Higgs bundles on a smooth projective curve have the same (stringy) class in the Grothendieck ring of rational Chow motives. On the level of Hodge numbers this was conjectured by Hausel and Thaddeus, and recently proven by Groechenig, Ziegler and the second author. To adapt their argument, which relies on p-adic integration, we use a version of motivic integration with values in rational Chow motives and the geometry of Neron models to evaluate such integrals on Hitchin fibers.

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希钦氏纤维的动力整合

证明了光滑投影曲线上扭曲的$\ mathm {SL}_n$和$\ mathm {PGL}_n$-希格斯束的模空间在有理Chow动机的Grothendieck环上具有相同的(弦)类。在霍奇数的层面上，这是由豪塞尔和塞迪厄斯推测出来的，最近由格罗切尼格、齐格勒和第二作者证明。为了适应他们的论点，这依赖于p进积分，我们使用了理性Chow动机值和Neron模型几何的动机积分版本来评估希钦纤维上的积分。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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