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 (Mi1 theorem 3.13). This proof is rather different from those of Strauch in St (theorem 3.3.1) and of Mieda in 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 Sh by using similar ideas here.
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