The relative trace formula approach for spherical varieties

Abstract

We present a general framework for the relative trace formula approach to the conjecture of Sakellaridis and Venkatesh on period integrals for spherical varieties over global fields.This approach is somehow well-known for experts but it seems lack of literature.Our approach is based on the spectrum isolation technique developed by Beuzart-Plessis et al. (2019) for number fields,which avoids the difficulty from the refined spectral expansion. This technique is also available in the function field case.