We introduce various affine Grassmannians, study their geometric properties, and give some
applications. We also discuss the geometric Satake equivalence. These are the expanded …

The goal of this paper is to show that the cohomology of compact unitary Shimura varieties is
concentrated in the middle degree and torsion-free, after localizing at a maximal ideal of the …

This is a companion paper of arXiv: 1601.03586. We study Coulomb branches of unframed
and framed quiver gauge theories of type $ ADE $. In the unframed case they are …

We endow the set of lattices in Q_p^n with a reasonable algebro-geometric structure. As a
result, we prove the representability of affine Grassmannians and establish the geometric …

We construct (cohomological) correspondences between mod $ p $ fibers of different
Shimura varieties and describe the fibers of these correspondences by studying irreducible …

This is the first in a series of papers devoted to describing the category of sheaves on the
affine flag manifold of a simple algebraic group in terms of the Langlands dual group. In the …

We give an interpretation of the path model of a representation (see 18) of a complex
semisimple algebraic group G in terms of the geometry of its affine Grassmannian. In this …

This paper concerns the dimensions of certain affine Deligne–Lusztig varieties, both in the
affine Grassmannian and in the affine flag manifold. Rapoport conjectured a formula for the …

These notes are devoted to a detailed exposition of the proof of the Geometric Satake
Equivalence for general coefficients by Mirković–Vilonen (Ann Math 166: 95–143, 2007) …

Affine Grassmannians and Geometric Satake Equivalences | International Mathematics
Research Notices | Oxford Academic Skip to Main Content Advertisement Oxford Academic …