On the Lefschetz trace formula for Lubin-Tate spaces

Details On the Lefschetz trace formula for Lubin-Tate spaces On the Lefschetz trace formula for Lubin-Tate spaces

2012-03-12

arxiv.org/abs/1203.2539v1

Mathematics

Algebraic Geometry

11 pages

Scientific paper

We reprove the Lefschetz trace formula for Lubin-Tate spaces, based on the locally finite cell decompositions of these spaces obtained in \cite{F3},\cite{F4}, and Mieda's theorem of Lefschetz trace formula for certain open adic spaces (\cite{Mi1} theorem 3.13). This proof is rather different from those in \cite{St} (theorem 3.3.1) and \cite{Mi1} (example 4.21), and is quite hopeful to generalized to some other Rapoport-Zink spaces as soon as there exist suitable cell decompositions, for example, we prove a Lefschetz trace formula for some unitary Rapoport-Zink spaces in \cite{Sh} by using similar ideas here.

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