Arithmetic intersection on GSpin Rapoport-Zink spaces

摘要

We prove an explicit formula for the arithmetic intersection number ofdiagonal cycles on GSpin Rapoport-Zink spaces in the minuscule case. This is alocal problem arising from the arithmetic Gan-Gross-Prasad conjecture fororthogonal Shimura varieties. Our formula can be viewed as an orthogonalcounterpart of the arithmetic-geometric side of the arithmetic fundamentallemma proved by Rapoport-Terstiege-Zhang in the minuscule case.