190 research outputs found
Igusa Stacks and the Cohomology of Shimura Varieties
No full textWe construct functorial Igusa stacks for all Hodge-type Shimura varieties, proving a conjecture of Scholze and extending earlier results of the fourth-named author for PEL-type Shimura varieties. Using the Igusa stack, we construct a sheaf on that controls the cohomology of the corresponding Shimura variety. We use this sheaf and the spectral action of Fargues-Scholze to prove a compatibility between the cohomology of Shimura varieties of Hodge type and the semisimple local Langlands correspondence of Fargues-Scholze, generalizing the Eichler-Shimura relation of Blasius-Rogawski to arbitrary level at . When the given Shimura variety is proper, we show moreover that the sheaf is perverse, which allows us to prove new torsion vanishing results for the cohomology of Shimura varieties
Igusa Stacks and the Cohomology of Shimura Varieties
No full textWe construct functorial Igusa stacks for all Hodge-type Shimura varieties, proving a conjecture of Scholze and extending earlier results of the fourth-named author for PEL-type Shimura varieties. Using the Igusa stack, we construct a sheaf on that controls the cohomology of the corresponding Shimura variety. We use this sheaf and the spectral action of Fargues-Scholze to prove a compatibility between the cohomology of Shimura varieties of Hodge type and the semisimple local Langlands correspondence of Fargues-Scholze, generalizing the Eichler-Shimura relation of Blasius-Rogawski to arbitrary level at . When the given Shimura variety is proper, we show moreover that the sheaf is perverse, which allows us to prove new torsion vanishing results for the cohomology of Shimura varieties.121 pages, comments welcome
Good and semi-stable reductions of Shimura varieties
No full textWe study variants of the local models constructed by the second author and Zhu and consider corresponding integral models of Shimura varieties of abelian type. We determine all cases of good, resp. of semi-stable, reduction under tame ramification hypotheses. Résumé (Bonne réduction et réduction semi-stable de variétés de Shimura) Nous étudions des variantes des modèles locaux introduits par le deuxième auteur et Zhu, et les modèles intégraux correspondants des variétés de Shimura de type abélien. Nous déterminons tous les cas de bonne réduction, resp. de réduction semi-stable, sous des hypothèses de ramification modéreé.link_to_subscribed_fulltex
TOPICS RELATED TO RSZ SHIMURA VARIETIES (Algebraic Number Theory and Related Topics)
No full textThis article is concerned with PEL unitary Shimura varieties and their integral models by Rapoport, Smithling and Zhang in relation to the arithmetic Gan-Gross-Prasad conjecture. We call these Shimura varieties RSZ Shimura varieties. We include two results here. One is about the comparison of these integral models with the ones by Kisin and Pappas. The other is about the curve case of the variant of the last conjecture formulated on the above Shimura varieties.This article bases itself on the talk by the author at 2022 RIMS workshop Algebraic Number Theory and Related Topics
TOPICS RELATED TO RSZ SHIMURA VARIETIES (Algebraic Number Theory and Related Topics)
No full textThis article bases itself on the talk by the author at 2022 RIMS workshop Algebraic Number Theory and Related Topics.This article is concerned with PEL unitary Shimura varieties and their integral models by Rapoport, Smithling and Zhang in relation to the arithmetic Gan-Gross-Prasad conjecture. We call these Shimura varieties RSZ Shimura varieties. We include two results here. One is about the comparison of these integral models with the ones by Kisin and Pappas. The other is about the curve case of the variant of the last conjecture formulated on the above Shimura varieties
Shimura curves in the Prym loci of ramified double covers
No full textWe study Shimura curves of PEL type in the space of polarised abelian varieties generically contained in the ramified Prym locus. We generalise to ramified double covers, the construction done by the first author with Colombo, Ghigi and Penegini in the unramified case and in the case of two ramification points. Namely, we construct families of double covers which are compatible with a fixed group action on the base curve. We only consider the case of one-dimensional families and where the quotient of the base curve by the group is the projective line. Using computer algebra we obtain 184 Shimura curves contained in the (ramified) Prym loci
Local models of Shimura varieties and a conjecture of Kottwitz
No full textWe give a group theoretic definition of “local models” as sought after in the theory of Shimura varieties. These are projective schemes over the integers of a p-adic local field that are expected to model the singularities of integral models of Shimura varieties with parahoric level structure. Our local models are certain mixed characteristic degenerations of Grassmannian varieties; they are obtained by extending constructions of Beilinson, Drinfeld, Gaitsgory and the second-named author to mixed characteristics and to the case of general (tamely ramified) reductive groups. We study the singularities of local models and hence also of the corresponding integral models of Shimura varieties. In particular, we study the monodromy (inertia) action and show a commutativity property for the sheaves of nearby cycles. As a result, we prove a conjecture of Kottwitz which asserts that the semi-simple trace of Frobenius on the nearby cycles gives a function which is central in the parahoric Hecke algebra
Supersymmetric Shimura operators and interpolation polynomials
No full textIn this dissertation, we give a partial super analog of a result obtained by Siddhartha Sahi and Genkai Zhang relating the Shimura operators and certain interpolation symmetric polynomials. We introduce the basic notions and give a survey of previous results in related areas. In particular, we study the pair (g = gl(2p|2q), k = gl(p|q)⊕gl(p|q)), define the supersymmetric Shimura operators in (U(g))^k, and prove that their images under the Harish-Chandra homomorphism are equal to specializations of Sergeev and Veselov's Type BC interpolation supersymmetric polynomials. This is our main theorem. We obtain results related to Harish-Chandra isomorphisms and generalized Verma modules along the way. Specifically, we show that it suffices to study certain elements in the center of U(g) and their actions on certain generalized Verma modules. We also offer a different approach to show the main theorem under the assumption that a family of irreducible g-modules is k-spherical. We introduce the notion of quasi-sphericity. With this, we prove the sphericity of these modules with the help of Kac modules in the case p=q=1. Many of the author’s results in this dissertation also appear in two earlier papers.Ph.D.Includes bibliographical reference
Fine scale eddies in turbulent Taylor-Couette flow up to Re 25 000
No full textReynolds number effects on fine scale eddies in the turbulent Taylor-Couette flow have been investigated by high accuracy direct numerical simulations from Re = 8000 to 25 000. The Reynolds number dependency of the mean torque changes near Re = 10 000, and the transition is closely linked to the turbulence characteristics. As the Reynolds number increases, the fine scale eddies are more densely populated and take more various tilting angles. The joint probability density function of the tilting angle and the radial position exhibits a preferential pattern corresponding to the large scale motion of Taylor vortices. The present results suggest that in this Reynolds number range, the fine scale eddies progressively prevail a large part of the domain, and their contribution to the fundamental statistics such as the Reynolds shear stress becomes more evident
Detection and Characterization of Mycoviruses in Arbuscular Mycorrhizal Fungi by Deep-Sequencing
No full textFungal viruses (mycoviruses) often have a significant impact not only on phenotypic expression of the host fungus but also on higher order biological interactions, e.g., conferring plant stress tolerance via an endophytic host fungus. Arbuscular mycorrhizal (AM) fungi in the phylum Glomeromycota associate with most land plants and supply mineral nutrients to the host plants. So far, little information about mycoviruses has been obtained in the fungi due to their obligate biotrophic nature. Here we provide a technical breakthrough, “two-step strategy” in combination with deep-sequencing, for virological study in AM fungi; dsRNA is first extracted and sequenced using material obtained from highly productive open pot culture, and then the presence of viruses is verified using pure material produced in the in vitro monoxenic culture. This approach enabled us to demonstrate the presence of several viruses for the first time from a glomeromycotan fungus
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