论文标题
lefschetz固定点定理
Lefschetz fixed point theorems for correspondences
论文作者
论文摘要
经典的lefschetz固定点定理指出，从歧管$ m $到本身的平滑地图$ f $计数的固定点的数量可以计算为交替的sum $ \ sum $ \ sum（-1）^k \ \ \ \ textrm {tr} f^*| _ {h^k（m） 1964年，在伍兹霍尔（Woods Hole）的一次会议上，Shimura猜想了一个Lefschetz的固定点定理，用于全态图，Atiyah和Bott证明并概括为椭圆形复合体的固定点定理。但是，在Shimura的回忆中，他的猜想比Holomorphic Lefschetz固定点定理更多。他说，他已经对全体形态通信做出了猜想，但他不记得这一说法。本文是对Shimura被遗忘的猜想的探索，首先是平滑的对应关系，然后以两种猜想的形式产生全体形态通信，最后以一个开放问题的形式出现，涉及两个品种上的霍明态矢量套件的扩展以及Hecke通讯的痕迹的计算。
The classical Lefschetz fixed point theorem states that the number of fixed points, counted with multiplicity $\pm 1$, of a smooth map $f$ from a manifold $M$ to itself can be calculated as the alternating sum $\sum (-1)^k \textrm{ tr } f^*|_{H^k(M)}$ of the trace of the induced homomorphism in cohomology. In 1964, at a conference in Woods Hole, Shimura conjectured a Lefschetz fixed point theorem for a holomorphic map, which Atiyah and Bott proved and generalized into a fixed point theorem for elliptic complexes. However, in Shimura's recollection, he had conjectured more than the holomorphic Lefschetz fixed point theorem. He said he had made a conjecture for a holomorphic correspondence, but he could not remember the statement. This paper is an exploration of Shimura's forgotten conjecture, first for a smooth correspondence, then for a holomorphic correspondence in the form of two conjectures and finally in the form of an open problem involving an extension to holomorphic vector bundles over two varieties and the calculation of the trace of a Hecke correspondence.
