Adelic Lefschetz formula for the action of a one-dimensional torus
Algebraic Geometry
2015-04-06 v1 Commutative Algebra
Number Theory
Abstract
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.
Keywords
Cite
@article{arxiv.math/0408058,
title = {Adelic Lefschetz formula for the action of a one-dimensional torus},
author = {Sergey Gorchinskiy and Alexey Parshin},
journal= {arXiv preprint arXiv:math/0408058},
year = {2015}
}
Comments
19 pages