arXiv math/04080582004-08-04math.AGmath.ACmath.NT

Adelic Lefschetz formula for the action of a one-dimensional torus

Sergey Gorchinskiy, Alexey Parshin

备注：: 19 pages
发表信息：: Proceedings of the St. Petersburg Mathematical Society, v. XI, Amer. Math. Soc. Transl. Ser. 2, 218, Amer. Math. Soc., Providence, RI, 2006, 31-48

英文摘要：

There exists a well-known Lefschetz formula for the number of fixed points in algebraic topology. In algebraic geometry, there exist cohomologies of coherent sheaves. It is natural to consider the same alternated sum of traces as in Lefschetz formula for cohomologies of sheaves. In the present paper, we consider the case of the action of a one-dimensional torus on a smooth projectve variety. Using theory of adelic complexes it becomes possible to rewrite coherent Lefschetz formula in a new compact form and then to prove it.

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