On the Lefschetz trace formula for Lubin-Tate spaces
Abstract
We reprove the Lefschetz trace formula for Lubin-Tate spaces, based on the locally finite cell decompositions of these spaces obtained by Fargues, 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 of Strauch in \cite{St} (theorem 3.3.1) and of Mieda in \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 proved a Lefschetz trace formula for some unitary Rapoport-Zink spaces in \cite{Sh} by using similar ideas here.
Keywords
Cite
@article{arxiv.1203.2539,
title = {On the Lefschetz trace formula for Lubin-Tate spaces},
author = {Xu Shen},
journal= {arXiv preprint arXiv:1203.2539},
year = {2012}
}
Comments
12 pages, the second part of the proof of theorem 3.3 is corrected; add remark 3.4, proposition 3.5 and a reference; type errors are corrected