On Quaternionic Unitary Rapoport–Zink Spaces with Parahoric Level Structures

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...

Cohomology of quaternionic Shimura varieties at parahoric levels

On the Siegel-weil Formula for Quaternionic Unitary Groups

We extend the Siegel-Weil formula to all quaternion dual pairs. Applications include the classification problem of skew hermitian forms over a quaternion algebra over a number field and a product formula for the weighted average of the representation numbers of a skew hermitian form by another skew hermitian form.

On Parahoric Subgroups

We give the proofs of some simple facts on parahoric subgroups and on Iwahori Weyl groups used in [H], [PR] and in [R]. 2000 Mathematics Subject Classification: Primary 11E95, 20G25; Secondary 22E20. Let G be a connected reductive group over a strictly henselian discretely valued field L. Kottwitz defines in [Ko] a functorial surjective homomorphism (1) κG : G(L) −→ X (Ẑ(G)). Here I = Gal(L̄/L) ...

Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem

A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given. It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolds. All conformal deformations sending the standard flat torsion-free quaternionic contac...