Atiyah-Segal theorem for Deligne-Mumford stacks and applications

IF 0.9 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry Pub Date : 2017-01-18 DOI:10.1090/jag/755

A. Krishna, Bhamidi Sreedhar

引用次数: 4

Abstract

We prove an Atiyah-Segal isomorphism for the higher K K -theory of coherent sheaves on quotient Deligne-Mumford stacks over C \mathbb {C} . As an application, we prove the Grothendieck-Riemann-Roch theorem for such stacks. This theorem establishes an isomorphism between the higher K K -theory of coherent sheaves on a Deligne-Mumford stack and the higher Chow groups of its inertia stack. Furthermore, this isomorphism is covariant for proper maps between Deligne-Mumford stacks.

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Deligne-Mumford堆栈的Atiya-Segal定理及其应用

我们证明了C\mathbb｛C｝上商Deligne-Mumford堆栈上相干槽轮的高K-理论的Atiyah-Segal同构。作为一个应用，我们证明了这类堆栈的Grothendieck-Riemann-Roch定理。该定理建立了Deligne-Mumford堆栈上相干槽轮的高K-理论与其惯性堆栈的高Chow群之间的同构。此外，对于Deligne-Mumford堆栈之间的适当映射，这种同构是协变的。

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

Journal of Algebraic Geometry 数学-数学

CiteScore

2.70

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.