Yang-Mills theory and Tamagawa numbers: the fascination of unexpected links in mathematics
Yang-Mills theory and Tamagawa numbers: the fascination of unexpected links in mathematics
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杨米尔斯理论和玉川数：数学中意想不到的联系的魅力
DOI：
10.1112/blms/bdn036
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发表时间：
2008
影响因子：
0.9
通讯作者：
Asok A
中科院分区：
文献类型：
--
作者：
Asok A
Atiyah和Bott将等变Morse理论应用于Yang-Mills泛函，计算了Riemann曲面上向量丛的模空间的Betti数，重新推导了由涉及SLN的Tamagawa数的算术方法得到的归纳公式.本文试图考察和扩展我们对杨-Mills理论和Tamagawa数之间的这种联系的理解，并解释过去三十年来研究ℂ上光滑射影曲线上的丛的模空间的奇异上同调的方法如何适用于𝔸1-同伦理论的背景，以研究代数闭域上这些模空间的模上同调.
Atiyah and Bott used equivariant Morse theory applied to the Yang–Mills functional to calculate the Betti numbers of moduli spaces of vector bundles over a Riemann surface, rederiving inductive formulae obtained from an arithmetic approach which involved the Tamagawa number of SLn. This article attempts to survey and extend our understanding of this link between Yang–Mills theory and Tamagawa numbers, and to explain how methods used over the last three decades to study the singular cohomology of moduli spaces of bundles on a smooth projective curve over ℂ can be adapted to the setting of 𝔸1‐homotopy theory to study the motivic cohomology of these moduli spaces over an algebraically closed field.