Representations of the Kottwitz gerbes
Representations of the Kottwitz gerbes
Dokument öffnen (781.2KB)Art der Hochschulschrift
DissertationPrüfungsdatum
07.03.2022Datum der Veröffentlichung
15.03.2022Erstgutachter
Scholze, PeterZweitgutachter
Blomer, ValentinMetadaten
Zur Langanzeige
Zitierbare Links 
Inhalt
Let F be a local or global field and let G be a linear algebraic group over F. We study Tannakian categories of representations of the Kottwitz gerbes Rep(Kt_F) and the functor G → B(F,G) defined by Kottwitz in [28]. In particular, we show that if F is the function field of a curve over F_q, then Rep(Kt_F) is equivalent to the category of Drinfeld isoshtukas. In the case of number fields, we establish the existence of various fibre functors on Rep(Kt_Q) and its subcategories and show that Scholze’s conjecture [41, Conjecture 9.5] follows from the full Tate conjecture over finite fields [47]
Schlagwörter
Kottwitz gerbes, Drinfeld isoshtukas, non-abelian cohomology, Tannakian categories, isocrystals
Klassifikation (DDC)
510 MathematikIakovenko, Sergei: Representations of the Kottwitz gerbes. - Bonn, 2022. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-65818
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-65818
@phdthesis{handle:20.500.11811/9675,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-65818,
author = {{Sergei Iakovenko}},
title = {Representations of the Kottwitz gerbes},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2022,
month = mar,
note = {Let F be a local or global field and let G be a linear algebraic group over F. We study Tannakian categories of representations of the Kottwitz gerbes Rep(Kt_F) and the functor G → B(F,G) defined by Kottwitz in [28]. In particular, we show that if F is the function field of a curve over F_q, then Rep(Kt_F) is equivalent to the category of Drinfeld isoshtukas. In the case of number fields, we establish the existence of various fibre functors on Rep(Kt_Q) and its subcategories and show that Scholze’s conjecture [41, Conjecture 9.5] follows from the full Tate conjecture over finite fields [47]},
url = {https://hdl.handle.net/20.500.11811/9675}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-65818,
author = {{Sergei Iakovenko}},
title = {Representations of the Kottwitz gerbes},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2022,
month = mar,
note = {Let F be a local or global field and let G be a linear algebraic group over F. We study Tannakian categories of representations of the Kottwitz gerbes Rep(Kt_F) and the functor G → B(F,G) defined by Kottwitz in [28]. In particular, we show that if F is the function field of a curve over F_q, then Rep(Kt_F) is equivalent to the category of Drinfeld isoshtukas. In the case of number fields, we establish the existence of various fibre functors on Rep(Kt_Q) and its subcategories and show that Scholze’s conjecture [41, Conjecture 9.5] follows from the full Tate conjecture over finite fields [47]},
url = {https://hdl.handle.net/20.500.11811/9675}
}
Die folgenden Nutzungsbestimmungen sind mit dieser Ressource verbunden:
