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You searched for subject:(Motivic AND adic realizationsof dg categories). Showing records 1 – 3 of 3 total matches.

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1. Pippi, Massimo. Catégories des singularités, factorisations matricielles et cycles évanescents : Categories of singularities, matrix factorizations and vanishing cycles.

Degree: Docteur es, Mathématiques et Applications, 2020, Université Toulouse III – Paul Sabatier

Le but de cette thèse est d'étudier les dg-catégories de singularités Sing(X, s), associées à des couples (X, s), où X est un schéma et s est une section d'un fibré vectoriel sur X. La dg-catégorie Sing(X, s) est définie comme le noyau du dg foncteur de Sing(X0) vers Sing(X) induit par l'image directe le long de l'inclusion du lieu de zéros (dérivé) X0 de s dans X. Dans une première partie, nous supposons que le fibré vectoriel est trivial de rang n. On démontre alors un théorème de structure pour Sing(X, s) dans le cas où X = Spec(B) est affine. Cet énoncé affirme que tout objet de Sing(X, s) est représenté par un complexe de B-modules concentré dans n+1 degrés. Lorsque n = 1, cet énoncé généralise l'équivalence d'Orlov , qui identifie Sing(X, s) avec la dg-catégorie des factorisations matricielles MF(X, s), au cas où s epsilon OX(X) n'est pas nécessairement plat. Dans une seconde partie, nous étudions la cohomologie l-adique de Sing(X, s) (définie par A. Blanc - M. Robalo - B. Toën and G. Vezzosi), où s est une section globale d'un fibré en droites. Pour cela, on introduit le faisceau l-adique des cycles évanescents invariantes par monodromie. En utilisant un théorème de D. Orlov généralisé par J. Burke et M. Walker, on calcule la réalisation l-adique de Sing(Spec(B), (f1 ,..., fn)) pour (f1 ,..., fn) epsilon Bn. Dans le dernier chapitre, nous introduisons les faisceaux l-adiques des cycles évanescents itérés pour un schéma sur un anneau de valuation discrète de rang 2. On relie ces faisceaux l-adiques à la réalisation l-adique des dg catégories de singularités des fibres prises sur certains sous-schémas fermés de la base.

The aim of this thesis is to study the dg categories of singularities Sing(X, s) of pairs (X, s), where X is a scheme and s is a global section of some vector bundle over X. Sing(X, s) is defined as the kernel of the dg functor from Sing(X0) to Sing(X) induced by the pushforward along the inclusion of the (derived) zero locus X0 of s in X. In the first part, we restrict ourselves to the case where the vector bundle is trivial. We prove a structure theorem for Sing(X, s) when X = Spec(B) is affine. Roughly, it tells us that every object in Sing(X, s) is represented by a complex of B-modules concentrated in n + 1 consecutive degrees (if s epsilon Bn). By specializing to the case n = 1, we generalize Orlov's theorem, which identifies Sing(X, s) with the dg category of matrix factorizations MF(X, s), to the case where s epsilon OX(X) is not flat. In the second part, we study the l-adic cohomology of Sing(X, s) (as defined by A. Blanc - M. Robalo - B. Toën and G. Vezzosi) when s is a global section of a line bundle. In order to do so, we introduce the l-adic sheaf of monodromy-invariant vanishing cycles. Using a theorem of D. Orlov generalized by J. Burke and M. Walker, we compute the l-adic realization of Sing(Spec(B), (f1 ,..., fn)) for (f1 ,..., fn) epsilon Bn. In the last chapter, we introduce the l-adic sheaves of iterated vanishing cycles of a scheme over a discrete valuation ring of rank 2.…

Advisors/Committee Members: Toën, Bertrand (thesis director), Vezzosi, Gabriele (thesis director).

Subjects/Keywords: Géométrie algébrique dérivée; Géométrie non-commutative; Cycles évanescents; Dg-catégories des singularités; Factorisations matricielles; Réalisations motivique et l-adique des dg-catégories; Derived algebraic geometry; Non-commutative geometry; Vanishing cycles; Dg categories of singularitie; Matrix factorizations; Motivic and`-adic realizationsof dg categories

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APA (6th Edition):

Pippi, M. (2020). Catégories des singularités, factorisations matricielles et cycles évanescents : Categories of singularities, matrix factorizations and vanishing cycles. (Doctoral Dissertation). Université Toulouse III – Paul Sabatier. Retrieved from http://www.theses.fr/2020TOU30049

Chicago Manual of Style (16th Edition):

Pippi, Massimo. “Catégories des singularités, factorisations matricielles et cycles évanescents : Categories of singularities, matrix factorizations and vanishing cycles.” 2020. Doctoral Dissertation, Université Toulouse III – Paul Sabatier. Accessed April 14, 2021. http://www.theses.fr/2020TOU30049.

MLA Handbook (7th Edition):

Pippi, Massimo. “Catégories des singularités, factorisations matricielles et cycles évanescents : Categories of singularities, matrix factorizations and vanishing cycles.” 2020. Web. 14 Apr 2021.

Vancouver:

Pippi M. Catégories des singularités, factorisations matricielles et cycles évanescents : Categories of singularities, matrix factorizations and vanishing cycles. [Internet] [Doctoral dissertation]. Université Toulouse III – Paul Sabatier; 2020. [cited 2021 Apr 14]. Available from: http://www.theses.fr/2020TOU30049.

Council of Science Editors:

Pippi M. Catégories des singularités, factorisations matricielles et cycles évanescents : Categories of singularities, matrix factorizations and vanishing cycles. [Doctoral Dissertation]. Université Toulouse III – Paul Sabatier; 2020. Available from: http://www.theses.fr/2020TOU30049


University of Michigan

2. Lawes, Elliot Wilson. Motivic integration and the regular Shalika germ.

Degree: PhD, Pure Sciences, 2003, University of Michigan

Let G denote an adjoint semisimple algebraic group defined over the integers. There is an analogy between Haar integration on the p-adic integer valued points of G and motivic integration on the complex power series valued points of G . A result of D. Shelstad from p-adic harmonic analysis states that the regular Shalika germ of such a group is an asymptotically constant function. In the present work it is demonstrated that the complex power series analogue of the regular Shalika germ is similarly an asymptotically constant function. There are three main steps involved in this demonstration. The first step is a description of certain affine schemes, together with morphisms from these schemes to the group. This allows the calculation of the complex power series analogue of the regular Shalika germ via motivic integration over such an affine scheme. The second step is the association of a less complicated shadow scheme to each such affine scheme. This association is achieved by analysis of the coordinate rings of the affine schemes. The third step is the use of the transformation rule from motivic integration. This is used to equate a motivic integral on each affine scheme with one on its associated shadow scheme. It is again used to equate the resulting motivic integrals on two different shadow schemes. This exactly means that the complex power series analogue of the regular Shalika germ is an asymptotically constant function. Advisors/Committee Members: Hales, Thomas C. (advisor), DeBacker, Stephen (advisor).

Subjects/Keywords: Haar Integration; Motivic Integration; P-adic; Regular; Shalika Germ

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Lawes, E. W. (2003). Motivic integration and the regular Shalika germ. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/123887

Chicago Manual of Style (16th Edition):

Lawes, Elliot Wilson. “Motivic integration and the regular Shalika germ.” 2003. Doctoral Dissertation, University of Michigan. Accessed April 14, 2021. http://hdl.handle.net/2027.42/123887.

MLA Handbook (7th Edition):

Lawes, Elliot Wilson. “Motivic integration and the regular Shalika germ.” 2003. Web. 14 Apr 2021.

Vancouver:

Lawes EW. Motivic integration and the regular Shalika germ. [Internet] [Doctoral dissertation]. University of Michigan; 2003. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/2027.42/123887.

Council of Science Editors:

Lawes EW. Motivic integration and the regular Shalika germ. [Doctoral Dissertation]. University of Michigan; 2003. Available from: http://hdl.handle.net/2027.42/123887


University of Michigan

3. Gordon, Julia. Some applications of motivic integration to the representation theory of p -adic groups.

Degree: PhD, Pure Sciences, 2003, University of Michigan

Let X be a variety over a field k. Motivic integration, introduced by M. Kontsevich in 1995, is a formal procedure that associates virtual Chow motives (or virtual equivalence classes of varieties) with subsets of X (k[[t]]), where k[[t]] is the ring of formal Taylor series with coefficients in k. It is analogous to a measure theory in every way except that the values of the motivic measure are not numbers but formal symbols associated with geometric objects such as Chow motives. In Part I of the thesis, a motivic Haar measure on groups of the form G(k((t))) is defined, where G is a reductive algebraic group defined over an algebraically closed field k of characteristic zero. The difficulty is contained in extending the original definition of motivic measure from the objects over formal Taylor series to the objects over formal Laurent series. This result is motivated by the hope that it would eventually help to develop a theory for groups of the form G(k((t))) that would be analogous to the representation theory of p-adic groups. Part II, which is independent of Part I, uses a different kind of motivic integration that specializes to p-adic integration for almost all primes p. Let G be the group Sp 2n or SO2n +1. Let F be a number field. Let o be a logical formula that defines a subset of G(Fv) for any finite place v. In Part II, the arithmetic motivic integration theory, which is due to J. Denef and F. Loeser, is used to deduce the existence of virtual Chow motives such that the trace of v-Frobenius action on them gives the values of the distribution characters of a certain class of representations of G( <blkbd>Fv</blkbd> ) on the set of regular topologically unipotent elements, for almost all finite places v of F. A variant of this statement for function fields is proved also. This gives a uniform (independent of p) way of thinking of the distribution characters, and illustrates their geometric nature. Advisors/Committee Members: Hales, Thomas C. (advisor), Griess, Robert L. (advisor).

Subjects/Keywords: Applications; Chow Motives; Frobenius Action; Motivic Integration; P-adic Groups; Representation Theory; Some

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Gordon, J. (2003). Some applications of motivic integration to the representation theory of p -adic groups. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/123392

Chicago Manual of Style (16th Edition):

Gordon, Julia. “Some applications of motivic integration to the representation theory of p -adic groups.” 2003. Doctoral Dissertation, University of Michigan. Accessed April 14, 2021. http://hdl.handle.net/2027.42/123392.

MLA Handbook (7th Edition):

Gordon, Julia. “Some applications of motivic integration to the representation theory of p -adic groups.” 2003. Web. 14 Apr 2021.

Vancouver:

Gordon J. Some applications of motivic integration to the representation theory of p -adic groups. [Internet] [Doctoral dissertation]. University of Michigan; 2003. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/2027.42/123392.

Council of Science Editors:

Gordon J. Some applications of motivic integration to the representation theory of p -adic groups. [Doctoral Dissertation]. University of Michigan; 2003. Available from: http://hdl.handle.net/2027.42/123392

.