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

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

2004-08-04

arxiv.org/abs/math/0408058v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

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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