Euler characteristic of certain affine flag varieties

1996 ◽  
Vol 1 (1-2) ◽  
pp. 35-39 ◽  
Author(s):  
C. Kenneth Fan
Keyword(s):  
Euler Characteristic ◽  
Flag Varieties ◽  
Affine Flag

scholarly journals Local models in the ramified case. III Unitary groups

2009 ◽  
Vol 8 (3) ◽  
pp. 507-564 ◽  
Author(s):  
G. Pappas ◽  
M. Rapoport
Keyword(s):  
Local Structure ◽  
Level Structure ◽  
Quadratic Extension ◽  
Unitary Groups ◽  
Shimura Varieties ◽  
Flag Varieties ◽  
Shimura Variety ◽  
Local Models ◽  
Affine Flag

AbstractWe continue our study of the reduction of PEL Shimura varieties with parahoric level structure at primespat which the group defining the Shimura variety ramifies. We describe ‘good’p-adic integral models of these Shimura varieties and study their étale local structure. In the present paper we mainly concentrate on the case of unitary groups for a ramified quadratic extension. Some of our results are applications of the theory of twisted affine flag varieties that we developed in a previous paper.

Affine flag varieties

2020 ◽  
pp. 191-206
Author(s):  
Peter Scholze ◽  
Jared Weinstein
Keyword(s):  
Group Scheme ◽  
Flag Variety ◽  
Flag Varieties ◽  
Connected Component ◽  
Witt Vector ◽  
Classical Definition ◽  
Definition Of ◽  
Affine Flag Variety ◽  
Affine Flag

This chapter reviews affine flag varieties. It generalizes some of the previous results to the case where G over Zp is a parahoric group scheme. In fact, slightly more generally, it allows the case that the special fiber is not connected, with connected component of the identity G? being a parahoric group scheme. This case comes up naturally in the classical definition of Rapoport-Zink spaces. The chapter first discusses the Witt vector affine flag variety over Fp. This is an increasing union of perfections of quasiprojective varieties along closed immersions. In the case that G° is parahoric, one gets ind-properness.

scholarly journals Twisted loop groups and their affine flag varieties

2008 ◽  
Vol 219 (1) ◽  
pp. 118-198 ◽  
Author(s):  
G. Pappas ◽  
M. Rapoport
Keyword(s):  
Flag Varieties ◽  
Loop Groups ◽  
Affine Flag

scholarly journals Degenerate Affine Flag Varieties and Quiver Grassmannians

2020 ◽  
Author(s):  
Alexander Pütz
Keyword(s):  
Flag Varieties ◽  
Rational Singularities ◽  
Quiver Grassmannians ◽  
Finite Dimensional ◽  
Irreducible Components ◽  
Affine Flag

AbstractWe study finite dimensional approximations to degenerate versions of affine flag varieties using quiver Grassmannians for cyclic quivers. We prove that they admit cellular decompositions parametrized by affine Dellac configurations, and that their irreducible components are normal Cohen-Macaulay varieties with rational singularities.

scholarly journals Tate motives on Witt vector affine flag varieties

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Timo Richarz ◽  
Jakob Scholbach
Keyword(s):  
Derived Categories ◽  
Flag Varieties ◽  
Witt Vector ◽  
Basic Properties ◽  
Finite Presentation ◽  
Affine Grassmannians ◽  
Recent Advances ◽  
Set Up ◽  
Affine Flag ◽  
Tate Motives

AbstractRelying on recent advances in the theory of motives we develop a general formalism for derived categories of motives with $${\mathbf{Q}}$$ Q -coefficients on perfect $$\infty $$ ∞ -prestacks. We construct Grothendieck’s six functors for motives over perfect (ind-)schemes perfectly of finite presentation. Following ideas of Soergel–Wendt, this is used to study basic properties of stratified Tate motives on Witt vector partial affine flag varieties. As an application we give a motivic refinement of Zhu’s geometric Satake equivalence for Witt vector affine Grassmannians in this set-up.

scholarly journals Goresky–MacPherson Calculus for the Affine Flag Varieties

2010 ◽  
Vol 62 (2) ◽  
pp. 473-480 ◽  
Author(s):  
Zhiwei Yun
Keyword(s):  
Fixed Point ◽  
Equivariant Cohomology ◽  
Flag Variety ◽  
Moment Map ◽  
Flag Varieties ◽  
The Moment ◽  
Affine Flag Variety ◽  
Affine Flag

AbstractWe use the fixed point arrangement technique developed by Goresky and MacPherson to calculate the part of the equivariant cohomology of the affine flag variety ℱ ℓ G generated by degree 2. We use this result to show that the vertices of the moment map image of ℱ ℓ G lie on a paraboloid.

scholarly journals Affine Deligne–Lusztig varieties in affine flag varieties

2010 ◽  
Vol 146 (5) ◽  
pp. 1339-1382 ◽  
Author(s):  
Ulrich Görtz ◽  
Thomas J. Haines ◽  
Robert E. Kottwitz ◽  
Daniel C. Reuman
Keyword(s):  
Level Structure ◽  
Flag Manifold ◽  
Shimura Varieties ◽  
Flag Varieties ◽  
Algorithmic Approach ◽  
Divisible Groups ◽  
Affine Flag

AbstractThis paper studies affine Deligne–Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those for Levi subgroups, and extends previous conjectures concerning their dimensions. We generalize the superset method, an algorithmic approach to the questions of non-emptiness and dimension. Our non-emptiness results apply equally well to the p-adic context and therefore relate to moduli of p-divisible groups and Shimura varieties with Iwahori level structure.

Sign in / Sign up

Export Citation Format

Share Document