DOCUMENTA MATHEMATICA, Vol. 15 (2010), 1049-1108

Shun Tang

A Lefschetz Fixed Point Formula for Singular Arithmetic Schemes with Smooth Generic Fibres

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 [31]. In particular, our result implies a fixed point formula which was conjectured by V. Maillot and D. Rössler in [25].

2010 Mathematics Subject Classification: 14C40, 14G40, 14L30, 58J20, 58J52

Keywords and Phrases: fixed point formula, singular arithmetic scheme, Arakelov geometry

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