Arithmetic Siegel–Weil formula at general nonsplit levels

Formulate and prove an arithmetic Siegel–Weil formula for unitary groups when the level K at nonsplit places is more general than the self-dual or almost self-dual parahoric levels used to construct regular integral models, thereby extending the identity between arithmetic intersection numbers and modified Eisenstein series to broader level structures.

Background

The current arithmetic Siegel–Weil results require choosing levels K that yield regular integral models at nonsplit places (e.g., self-dual or almost self-dual lattices), limiting adelic generality. The author points out the related open problem of developing an arithmetic Siegel–Weil formula at more general nonsplit levels; partial formulations exist for minuscule parahoric levels, but a comprehensive theory remains open.