A Lefschetz fixed point formula for singular arithmetic schemes with smooth generic fibres

Details A Lefschetz fixed point formula for singular arithmetic schemes with smooth generic fibres A Lefschetz fixed point formula for singular arithmetic schemes with smooth generic fibres

2010-02-10

arxiv.org/abs/1002.2142v3

Mathematics

Algebraic Geometry

60 pages

Scientific paper

In this article, we consider singular equivariant arithmetic schemes whose generic fibres are smooth. For such schemes, we prove a relative fixed point formula of Lefschetz type in the context of Arakelov geometry. This formula is an analog, in the arithmetic case, of the Lefschetz formula proved by R. W. Thomason. In particular, our result implies a fixed point formula which was conjectured by V. Maillot and D. R\"{o}ssler.

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