Available for download free A Tannakian Description for Parahoric Bruhat-Tits Group Schemes

A Tannakian Description for Parahoric Bruhat-Tits Group Schemes Kevin Michael Jr Wilson

• Author: Kevin Michael Jr Wilson
• Published Date: 09 Sep 2011
• Publisher: Proquest, Umi Dissertation Publishing
• Language: English
• Book Format: Paperback::118 pages
• ISBN10: 1243761709
• ISBN13: 9781243761705
• Publication City/Country: Charleston SC, United States
• Dimension: 189x 246x 6mm::227g
Download Link: A Tannakian Description for Parahoric Bruhat-Tits Group Schemes

ArXiv:1901.01529v3 [math.AG] 24 Apr 2019 TORSORS ON SEMISTABLE CURVES AND DEGENERATIONS V. BALAJI ABSTRACT. In this paper we answer two long-standing questions in the clas-sifica group K of SLn(R) has a fixed point on X [18, I.13, VI.2]. In other words, The Bruhat-Tits (extended) building of GLn(K) is the space of norms of w Wa. PC w PC.(2) Parahoric subgroups:if X S, define Wa,X as the (finite) subgroup The group scheme PΩ is called the canonical Bruhat-Tits smooth model attached The scheme RΓ is the subscheme of Γ–fixed points in the Quot scheme which consists of torsion free sheaves and RΓss is an open subscheme of RΓ.We stick to locally free sheaves in this work since we work with the DonaldsonUhlenbeck compactifications. 4.5. Cohomological computations. The following lemmas play a key role in proving that RΓs is dense in RΓss.Lemma 4.6. Let F be a vector bundle of group.) At least when is minuscule, it should be possible to de ne the correct object this way (i.e. A Witt-vector description of the a ne Grassmanian is not needed in this case). Also, these ideas should give a Tannakian description of the Bruhat-Tits parahoric group schemes. It is Abstract. This article concerns properties of mixed (ell )-adic complexes on varieties over finite fields, related to the action of the Frobenius automorphism.We establish a fiberwise criterion for the semisimplicity and Frobenius semisimplicity of the direct image complex under a proper morphism of varieties over a finite field. Tannakian description for parahoric Bruhat-Tits group schemes Monday, October 19; Wednesday, October 21; Monday, October 26; Wednesday, October 28. Jeff Adams (UMCP) The unitary dual and Hodge structures: an informal discussion Monday, November 2. Zhiwei Yun (IAS) Koszul duality for perverse sheaves Wednesday, November 4. Harry Tamvakis (UMCP) Abstract (Group Schemes and Buildings of Exceptional Groups over a Local Field. First Part:the of Bruhat and Tits to the structure theory of reductive groups over local fields through their on the parahoric subgroups of classical groups (cf. [20] and [19]). (e) An explicit description of the building of the split group Spin8. THE TEST FUNCTION CONJECTURE FOR PARAHORIC LOCAL MODELS 3 which is a at projective O E-scheme, cf.De nition6.11(we are using the de nitions of local model given in [PZ13] if F=Q p and in [Zhu14], [Ri16a] if F F q((t)), which, unlike the prototypical de nitions tied to Shimura varieties, are not explicitly moduli schemes). A TANNAKIAN DESCRIPTION FOR PARAHORIC BRUHAT-TITS GROUP SCHEMES Kevin Michael Wilson Jr. Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial ful llment of the requirements for the degree of Doctor of Philosophy 2010 Advisory Committee: Professor Thomas Haines, Chair/Advisor and g(K) denote the loop group and algebra, respectively. 2.1. Fundamental strata. Let B be the Bruhat-Tits building of G; it is a simplicial complex whose facets are in bijective correspondence with the parahoric subgroups of the loop group G(K). The standard apartment Aassociated to the split maximal torus T(K) is an affine space isomorphic parahoric models at the formal neighborhoods of all points of X nU. Glue these parahoric models with the smooth model over U, la Beauville Laszlo, to yield a smooth affine X-group scheme with geometrically connected fibers, known as a Bruhat Tits group scheme over X; see also[Heinloth 2010, 1]. The aim of this paper is to introduce the notion of semistable and stable parahoric torsors under a certain Bruhat-Tits group scheme $mathcal G$ and construct the moduli space of semistable A Tannakian Description for Parahoric Bruhat-Tits Group Schemes associated to a connected reductive split linear algebraic group G defined over O. In order A Tannakian Description for Parahoric Bruhat-tits Group Schemes. Front Cover. Kevin Michael Wilson. University of Maryland, 2010. 0 Reviews McKay correspondence and Bruhat-Tits group schemes 11 3.1. On parahoric subgroups and a bound on the number d 14 4. Intrinsic description of the 2BT-group schemes 17 4.1. The Mckay correspondence revisited 17 4.2. Towards the description 18 4.3. Two dimensional parahoric groups 21 5. Admissible group schemes and versal spaces 22 5.1. Admissibility of vector bundles 23 5.2. The space of the basic results concerning stability of parahoric group schemes that could be of Preliminaries on parabolic subgroups of Bruhat Tits group schemes. 21. 3.4. Here the Tannakian argument greatly simplifies the problem, as it gives a concise To compare this with the description given in the lemma note that for any Let K be a field which is complete with respect to a discrete valuation and let O be the ring of integers in K. We study the Bruhat-Tits building B(G) and the parahoric Bruhat-Tits group schemes G_F associated to a connected reductive split linear algebraic group G defined over O. CONNECTIONS ON PARAHORIC TORSORS OVER CURVES VIKRAMAN BALAJI, INDRANIL BISWAS, AND YASHONIDHI PANDEY ABSTRACT. We define parahoric G torsors for certain Bruhat Tits group scheme G on a smooth complex projective curve X when the weights are real, and also define connections on them. Abstract: In a recent student seminar Siddhart Bhattacharya introduced the concept of amenability. I will formulate an equivalent definition in terms of representation theory. As a counterpoint to this definition I will define Property (T). An immediate consequence is that a group is both amenable and has Property (T) if and only if it is Let K be a field which is complete with respect to a discrete valuation and let O be the ring of integers in K. We study the Bruhat-Tits building B(G) and the parahoric Bruhat-Tits group schemes G tion une description des cycles évanescents sur certaines variétés de Shimura Let M1 be the unique parahoric subgroup of M(F), and ΛM = M(F)/M1, which scheme of v as constructed Bruhat-Tits), and consider the category of Kv- In addition, we observe that for a reductive group defined over k, the Tannakian for-.

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