Concentration theorem and relative fixed point formula of Lefschetz type in Arakelov geometry

Details Concentration theorem and relative fixed point formula of Lefschetz type in Arakelov geometry Concentration theorem and relative fixed point formula of Lefschetz type in Arakelov geometry

2010-02-09

arxiv.org/abs/1002.1903v4

Mathematics

Algebraic Geometry

30 pages

Scientific paper

In this paper we prove a concentration theorem for arithmetic $K_0$-theory, this theorem can be viewed as an analog of R. Thomason's result in the arithmetic case. We will use this arithmetic concentration theorem to prove a relative fixed point formula of Lefschetz type in the context of Arakelov geometry. Such a formula was conjectured of a slightly stronger form by K. K\"{o}hler and D. Roessler and they also gave a correct route of its proof. Nevertheless our new proof is much simpler since it looks more natural and it doesn't involve too many complicated computations.

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