scholarly journals COMPACTIFICATIONS OF SUBSCHEMES OF INTEGRAL MODELS OF SHIMURA VARIETIES

2018 ◽  
Vol 6 ◽  
Author(s):  
KAI-WEN LAN ◽  
BENOÎT STROH
Keyword(s):  
Characteristic Zero ◽  
Shimura Varieties ◽  
Mixed Characteristic ◽  
Coherent Sheaves ◽  
Local Structures ◽  
As If

We study several kinds of subschemes of mixed characteristic models of Shimura varieties which admit good (partial) toroidal and minimal compactifications, with familiar boundary stratifications and formal local structures, as if they were Shimura varieties in characteristic zero. We also generalize Koecher’s principle and the relative vanishing of subcanonical extensions for coherent sheaves, and Pink’s and Morel’s formulas for étale sheaves, to the context of such subschemes.

scholarly journals On Some Generalized Rapoport–Zink Spaces

2019 ◽  
Vol 72 (5) ◽  
pp. 1111-1187
Author(s):  
Xu Shen
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
K3 Surfaces ◽  
Connected Components ◽  
Shimura Varieties ◽  
Reductive Groups ◽  
Mixed Characteristic ◽  
Special Fibers ◽  
Type Spaces ◽  
Local Invariants

AbstractWe enlarge the class of Rapoport–Zink spaces of Hodge type by modifying the centers of the associated $p$-adic reductive groups. Such obtained Rapoport–Zink spaces are said to be of abelian type. The class of Rapoport–Zink spaces of abelian type is strictly larger than the class of Rapoport–Zink spaces of Hodge type, but the two type spaces are closely related as having isomorphic connected components. The rigid analytic generic fibers of Rapoport–Zink spaces of abelian type can be viewed as moduli spaces of local $G$-shtukas in mixed characteristic in the sense of Scholze.We prove that Shimura varieties of abelian type can be uniformized by the associated Rapoport–Zink spaces of abelian type. We construct and study the Ekedahl–Oort stratifications for the special fibers of Rapoport–Zink spaces of abelian type. As an application, we deduce a Rapoport–Zink type uniformization for the supersingular locus of the moduli space of polarized K3 surfaces in mixed characteristic. Moreover, we show that the Artin invariants of supersingular K3 surfaces are related to some purely local invariants.

scholarly journals Stable Conjugacy: Definitions and Lemmas

1979 ◽  
Vol 31 (4) ◽  
pp. 700-725 ◽  
Author(s):  
R. P. Langlands
Keyword(s):  
Trace Formula ◽  
Characteristic Zero ◽  
Present Note ◽  
Zeta Functions ◽  
Base Change ◽  
Shimura Varieties ◽  
Reductive Groups ◽  
Typical Problem

The purpose of the present note is to introduce some notions useful for applications of the trace formula to the study of the principle of functoriality, including base change, and to the study of zeta-functions of Shimura varieties. In order to avoid disconcerting technical digressions I shall work with reductive groups over fields of characteristic zero, but the second assumption is only a matter of convenience, for the problems caused by inseparability are not serious.The difficulties with which the trace formula confronts us are manifold. Most of them arise from the non-compactness of the quotient and will not concern us here. Others are primarily arithmetic and occur even when the quotient is compact. To see how they arise, we consider a typical problem.

scholarly journals Which abelian tensor categories are geometric?

2018 ◽  
Vol 2018 (734) ◽  
pp. 145-186 ◽  
Author(s):  
Daniel Schäppi
Keyword(s):  
Characteristic Zero ◽  
Intrinsic Properties ◽  
Tensor Categories ◽  
Projective Varieties ◽  
Coherent Sheaves ◽  
Geometric Objects ◽  
Necessary And Sufficient ◽  
Tannaka Duality ◽  
Tannakian Categories

AbstractFor a large class of geometric objects, the passage to categories of quasi-coherent sheaves provides an embedding in the 2-category of abelian tensor categories. The notion of weakly Tannakian categories introduced by the author gives a characterization of tensor categories in the image of this embedding.However, this notion requires additional structure to be present, namely a fiber functor. For the case of classical Tannakian categories in characteristic zero, Deligne has found intrinsic properties—expressible entirely within the language of tensor categories—which are necessary and sufficient for the existence of a fiber functor. In this paper we generalize Deligne’s result to weakly Tannakian categories in characteristic zero. The class of geometric objects whose tensor categories of quasi-coherent sheaves can be recognized in this manner includes both the gerbes arising in classical Tannaka duality and more classical geometric objects such as projective varieties over a field of characteristic zero.Our proof uses a different perspective on fiber functors, which we formalize through the notion of geometric tensor categories. A second application of this perspective allows us to describe categories of quasi-coherent sheaves on fiber products.

scholarly journals Non-archimedean hyperbolicity and applications

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ariyan Javanpeykar ◽  
Alberto Vezzani
Keyword(s):  
Abelian Variety ◽  
Moduli Space ◽  
Characteristic Zero ◽  
Projective Variety ◽  
Uniformization Theorem ◽  
Mixed Characteristic ◽  
Analytic Varieties ◽  
Fixed Part ◽  
Natural Analogues ◽  
Constant Morphism

Abstract Inspired by the work of Cherry, we introduce and study a new notion of Brody hyperbolicity for rigid analytic varieties over a non-archimedean field K of characteristic zero. We use this notion of hyperbolicity to show the following algebraic statement: if a projective variety admits a non-constant morphism from an abelian variety, then so does any specialization of it. As an application of this result, we show that the moduli space of abelian varieties is K-analytically Brody hyperbolic in equal characteristic 0. These two results are predicted by the Green–Griffiths–Lang conjecture on hyperbolic varieties and its natural analogues for non-archimedean hyperbolicity. Finally, we use Scholze’s uniformization theorem to prove that the aforementioned moduli space satisfies a non-archimedean analogue of the “Theorem of the Fixed Part” in mixed characteristic.

Improvement of an artificial test substrate technique for evaluation of em immunocytochemical labeling

1987 ◽  
Vol 45 ◽  
pp. 762-763
Author(s):  
G. D. Gagne ◽  
M. F. Miller
Keyword(s):  
Bovine Serum Albumin ◽  
Serum Albumin ◽  
Bovine Serum ◽  
Artificial Substrate ◽  
Chemical Fixation ◽  
As If

We recently described an artificial substrate system which could be used to optimize labeling parameters in EM immunocytochemistry (ICC). The system utilizes blocks of glutaraldehyde polymerized bovine serum albumin (BSA) into which an antigen is incorporated by a soaking procedure. The resulting antigen impregnated blocks can then be fixed and embedded as if they are pieces of tissue and the effects of fixation, embedding and other parameters on the ability of incorporated antigen to be immunocyto-chemically labeled can then be assessed. In developing this system further, we discovered that the BSA substrate can also be dried and then sectioned for immunolabeling with or without prior chemical fixation and without exposing the antigen to embedding reagents. The effects of fixation and embedding protocols can thus be evaluated separately.

Sign in / Sign up

Export Citation Format

Share Document