On the arithmetic Siegel–Weil formula for GSpin Shimura varieties

We formulate and prove a local arithmetic Siegel–Weil formula for GSpin Rapoport–Zink spaces, which is precise identity between the intersection numbers of special cycles on spaces derivatives representation densities quadratic forms. As first application, we semi-global as conjectured by Kudla, relates Shimura varieties at place good reduction central nonsingular Fourier coefficients incoherent Siegel Eisenstein series.