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Representation Theory and Arithmetic Statistics of Generalized Configuration Spaces
Başlık:
Representation Theory and Arithmetic Statistics of Generalized Configuration Spaces
Yazar:
Casto, Kevin, author.
ISBN:
9780438088535
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (84 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Advisors: Benson Farb Committee members: Victor Ginzburg.
Özet:
In this thesis, we extend the work of Church-Ellenberg-Farb on FI-modules, representation stability of configuration spaces, and arithmetic statistics. We study two generalizations of the category FI: namely FIG for G a group, first studied by Sam-Snowden, and FI m, first studied by Gadish. We use these to study two types of generalized configuration spaces: the orbit configuration spaces Conf Gn(M), associated to a G-cover M, and the space of ordered 0-cycles Zn(d1,...dm) (X) introduced by Farb-Wolfson-Wood. After establishing basic properties of FIG- and FI m-modules, we obtain representation stability results for the cohomology of these generalized configuration spaces. We establish subexponential bounds on the growth of unstable cohomology, and the Grothendieck-Lefschetz trace formula then allows us to translate these topological stability phenomena to stabilization of arithmetic statistics for generalized configuration spaces over finite fields.
Notlar:
School code: 0330
Konu Başlığı:
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(693654.1) | 693654-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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