Header

UZH-Logo

Maintenance Infos

Traces, homotopy theory, and motivic Galois groups


Gallauer Alves de Souza, Martin. Traces, homotopy theory, and motivic Galois groups. 2015, University of Zurich, Faculty of Science.

Abstract

This thesis consists of two independent parts. In the first part we ask how traces in monoidal categories behave under homotopical operations. In order to investigate this question we define traces in closedmonoidal derivators and establish some of their properties.
In the stable setting we derive an explicit formula for the trace of the homotopy colimit over finite categories in which every endomorphism is invertible. In the second part, we study motives of algebraic varieties over a subfield of the complex numbers, as defined by Nori on the one hand and by Voevodsky, Levine, and Hanamura on the other. Ayoub attached to the latter theory a motivic Galois group using the Betti realization, based on a weak Tannakian formalism. Our main theorem states that Nori’s and Ayoub’s motivic Galois groups are isomorphic. In the process of proving this result we construct well-behaved functors relating the two theories which are of independent interest.

Abstract

This thesis consists of two independent parts. In the first part we ask how traces in monoidal categories behave under homotopical operations. In order to investigate this question we define traces in closedmonoidal derivators and establish some of their properties.
In the stable setting we derive an explicit formula for the trace of the homotopy colimit over finite categories in which every endomorphism is invertible. In the second part, we study motives of algebraic varieties over a subfield of the complex numbers, as defined by Nori on the one hand and by Voevodsky, Levine, and Hanamura on the other. Ayoub attached to the latter theory a motivic Galois group using the Betti realization, based on a weak Tannakian formalism. Our main theorem states that Nori’s and Ayoub’s motivic Galois groups are isomorphic. In the process of proving this result we construct well-behaved functors relating the two theories which are of independent interest.

Statistics

Downloads

0 downloads since deposited on 03 Feb 2016
0 downloads since 12 months

Additional indexing

Item Type:Dissertation
Referees:Ayoub Joseph, Kresch Andrew, Okonek Christian
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2015
Deposited On:03 Feb 2016 10:52
Last Modified:22 Sep 2016 11:41
Number of Pages:127
Official URL:http://www.recherche-portal.ch/ZAD:default_scope:ebi01_prod010582930

Download

Preview Icon on Download
Content: Accepted Version
Language: English
Filetype: PDF - Registered users only
Size: 1MB

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations