# Congruence relations of GSpin Shimura varieties

## TL;DR

This paper proves a key congruence relation for simple GSpin Shimura varieties, extending previous results and contributing to the understanding of their arithmetic properties.

## Contribution

It establishes the Chai-Faltings version of the Eichler-Shimura congruence relation specifically for simple GSpin Shimura varieties, expanding prior work by other researchers.

## Key findings

- Proved the Eichler-Shimura congruence relation for GSpin Shimura varieties.
- Extended previous results to a broader class of Shimura varieties.
- Contributed to the arithmetic theory of GSpin Shimura varieties.

## Abstract

In these notes I proved the Chai-Faltings version of Eichler-Shimura congruence relation for simple GSpin Shimura varieties. This extends the results by Bueltel, Wedhorn and Koskivirta.