scholarly journals G 2 and some exceptional Witt vector identities

2017 ◽  
Vol 47 ◽  
pp. 125-144
Author(s):  
Nicholas M. Katz
Keyword(s):  
Witt Vector

scholarly journals Projectivity of the Witt vector affine Grassmannian

2016 ◽  
Vol 209 (2) ◽  
pp. 329-423 ◽  
Author(s):  
Bhargav Bhatt ◽  
Peter Scholze
Keyword(s):  
Witt Vector ◽  
Affine Grassmannian

scholarly journals On Witt vector cohomology for singular varieties

2007 ◽  
Vol 143 (02) ◽  
pp. 363-392 ◽  
Author(s):  
Pierre Berthelot ◽  
Spencer Bloch ◽  
Hélène Esnault
Keyword(s):  
Witt Vector ◽  
Singular Varieties

scholarly journals On the Frobenius stable part of Witt vector cohomology

2011 ◽  
Vol 354 (3) ◽  
pp. 1177-1200 ◽  
Author(s):  
Andre Chatzistamatiou
Keyword(s):  
Witt Vector ◽  
Stable Part

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.

Extending torsors on the punctured Spec(A inf)

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Johannes Anschütz
Keyword(s):  
Flag Variety ◽  
Full Generality ◽  
Witt Vector ◽  
Affine Grassmannian ◽  
Group Schemes ◽  
Affine Flag Variety ◽  
Affine Flag

Abstract We prove that torsors under parahoric group schemes on the punctured spectrum of Fontaine’s ring A inf {A_{\mathrm{inf}}} , extend to the whole spectrum. Using descent we can extend a similar result for the ring 𝔖 {\mathfrak{S}} of Kisin and Pappas to full generality. Moreover, we treat similarly the case of equal characteristic. As applications we extend results of Ivanov on exactness of the loop functor and present the construction of a canonical specialization map from the B dR + {B^{+}_{\mathrm{dR}}} -affine Grassmannian to the Witt vector affine flag variety.

scholarly journals Dual Complex of Log Fano Pairs and Its Application to Witt Vector Cohomology

2020 ◽  
Author(s):  
Yusuke Nakamura
Keyword(s):  
Rational Point ◽  
Vanishing Theorem ◽  
Witt Vector ◽  
Dual Complex

Abstract We prove the contractibility of the dual complexes of weak log Fano pairs. As applications, we obtain a vanishing theorem of Witt vector cohomology of Ambro–Fujino type and a rational point formula in Dimension 3.

scholarly journals The Burnside ring of profinite groups and the Witt vector construction

1988 ◽  
Vol 70 (1) ◽  
pp. 87-132 ◽  
Author(s):  
Andreas W.M. Dress ◽  
Christian Siebeneicher
Keyword(s):  
Profinite Groups ◽  
Burnside Ring ◽  
Witt Vector ◽  
Vector Construction

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.

-DISPLAYS AND RAPOPORT–ZINK SPACES

2018 ◽  
Vol 19 (4) ◽  
pp. 1211-1257 ◽  
Author(s):  
O. Bültel ◽  
G. Pappas
Keyword(s):  
Reductive Group ◽  
Witt Vector ◽  
Formal Schemes ◽  
Divisible Groups

Let $(G,\unicode[STIX]{x1D707})$ be a pair of a reductive group $G$ over the $p$-adic integers and a minuscule cocharacter $\unicode[STIX]{x1D707}$ of $G$ defined over an unramified extension. We introduce and study ‘$(G,\unicode[STIX]{x1D707})$-displays’ which generalize Zink’s Witt vector displays. We use these to define certain Rapoport–Zink formal schemes purely group theoretically, i.e. without $p$-divisible groups.

scholarly journals Trace formula for Witt vector rings

2017 ◽  
Vol 355 (6) ◽  
pp. 601-606
Author(s):  
Benzaghou Benali ◽  
Mokhfi Siham
Keyword(s):  
Trace Formula ◽  
Witt Vector
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