On the Voevodsky Motive of the Moduli Stack of Vector Bundles on a Curve

IF 0.6 4区 数学 Q3 MATHEMATICS Quarterly Journal of Mathematics Pub Date : 2020-12-01 DOI:10.1093/qmathj/haaa023
Victoria Hoskins;Simon Pepin Lehalleur
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引用次数: 15

Abstract

We define and study the motive of the moduli stack of vector bundles of fixed rank and degree over a smooth projective curve in Voevodsky’s category of motives. We prove that this motive can be written as a homotopy colimit of motives of smooth projective Quot schemes of torsion quotients of sums of line bundles on the curve. When working with rational coefficients, we prove that the motive of the stack of bundles lies in the localizing tensor subcategory generated by the motive of the curve, using Białynicki-Birula decompositions of these Quot schemes. We conjecture a formula for the motive of this stack, inspired by the work of Atiyah and Bott on the topology of the classifying space of the gauge group, and we prove this conjecture modulo a conjecture on the intersection theory of the Quot schemes.
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曲线上向量束模堆的Voevodsky动机
在Voevodsky的动机范畴中,我们定义并研究了光滑投影曲线上固定秩和阶的向量束的模堆栈的动机。我们证明了这个动机可以写成曲线上线束和的扭商的光滑投影商格式的动机的一个同伦群。当使用有理系数时,我们使用这些Quot方案的Białynicki-Birula分解,证明了丛堆栈的动机位于由曲线的动机生成的局部化张量子类别中。受Atiyah和Bott关于规范群分类空间拓扑的工作的启发,我们猜想了这个堆栈的动机的一个公式,并在Quot格式的交集理论上证明了这个猜想的模a猜想。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
36
审稿时长
6-12 weeks
期刊介绍: The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. All major areas of pure mathematics are represented on the editorial board.
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