# Arithmetic intersection on GSpin Rapoport-Zink spaces

## TL;DR

This paper derives an explicit formula for arithmetic intersection numbers of diagonal cycles on GSpin Rapoport-Zink spaces, advancing understanding in the local context of the arithmetic Gan-Gross-Prasad conjecture for orthogonal Shimura varieties.

## Contribution

It provides a new explicit formula for intersection numbers in the minuscule case, extending the arithmetic fundamental lemma to GSpin Rapoport-Zink spaces.

## Key findings

- Explicit formula for intersection numbers derived
- Connects to the arithmetic Gan-Gross-Prasad conjecture
- Extends the arithmetic fundamental lemma to a new setting

## Abstract

We prove an explicit formula for the arithmetic intersection number of diagonal cycles on GSpin Rapoport-Zink spaces in the minuscule case. This is a local problem arising from the arithmetic Gan-Gross-Prasad conjecture for orthogonal Shimura varieties. Our formula can be viewed as an orthogonal counterpart of the arithmetic-geometric side of the arithmetic fundamental lemma proved by Rapoport-Terstiege-Zhang in the minuscule case.