Special cycles on unitary Shimura varieties with minuscule parahoric level structure

Shimura Varieties with Parahoric Level

This survey article is intended to introduce the reader to several important concepts relating to Shimura varieties with parahoric level structure at p. The main tool is the Rapoport-Zink local model [RZ], which plays an important role in several aspects of the theory. We discuss local models attached to general linear and symplectic groups, and we illustrate their relation to Shimura varieties...

Special Cycles on Unitary Shimura Varieties I. Unramified Local Theory

A relation between a generating series constructed from arithmetic cycles on an integral model of a Shimura curve and the derivative of a Siegel Eisenstein series of genus 2 was established by one of us in [9]. There, the hope is expressed that such a relation should hold in greater generality for integral models of Shimura varieties attached to orthogonal groups of signature (2, n − 2) for any...

Rankin-selberg L-functions and Cycles on Unitary Shimura Varieties

Reduction of Shimura varieties at parahoric levels

Modularity of Generating Functions of Special Cycles on Shimura Varieties

Modularity of Generating functions of Special Cycles on Shimura Varieties