Local Models For Rapoport-Zink Spaces For Local P-Shtukas

TL;DR

This paper develops local models for Rapoport-Zink spaces associated with local P-shtukas, enhancing understanding of their geometry and applications in formal nearby cycles and Frobenius trace computations.

Contribution

It introduces the construction of local models for Rapoport-Zink spaces for local P-shtukas, complementing existing global models and advancing the geometric analysis of these moduli spaces.

Findings

Construction of local models for Rapoport-Zink spaces for local P-shtukas

Analysis of formal nearby cycles associated with these spaces

Results on semi-simple trace of Frobenius on related sheaves

Abstract

This article provides a ``local'' complementary to the previous results concerning the local models for the moduli stacks of ``global'' $G$-shtukas. Here we study the geometry of Rapoport-Zink spaces for local $P$-shtukas by constructing local models for them. We further discuss certain applications, including some results related to the theory of formal nearby cycles associated to these spaces and the semi-simple trace of Frobenius on the corresponding sheaves.