Tang, Shun

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

Doc. Math., J. DMV 15, 1049-1108 (2010)


Summary: 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].

Mathematics Subject Classification

14C40, 14G40, 14L30, 58J20, 58J52


fixed point formula, singular arithmetic scheme, Arakelov geometry