# Shtukas adiques, modifications et applications

## TL;DR

This paper explores the modifications of vector bundles on the Fargues-Fontaine curve to establish a geometric relation between Lubin-Tate towers and certain Rapoport-Zink spaces, leading to cohomology computations.

## Contribution

It introduces a geometric formula linking Lubin-Tate towers with basic unramified Rapoport-Zink spaces of EL type, advancing understanding of their structure and cohomology.

## Key findings

- Established a geometric formula relating Lubin-Tate towers and Rapoport-Zink spaces.
- Computed the cohomology groups of specific Rapoport-Zink spaces.
- Enhanced the understanding of vector bundle modifications on the Fargues-Fontaine curve.

## Abstract

In this paper, via the study of the modifications of vector bundles on the Fargues-Fontaine curve, we prove a geometric formula relating the Lubin-Tate towers with the simple basic unramified Rapoport-Zink spaces of EL type of signature $ (1, n-1), (p_1, q_1), \cdots, (p_k, q_k) $ where $ p_iq_i = 0 $. In particular, we deduce the computation of the cohomology groups of the latter.