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On the kernel of the reciprocity map of varieties over local fields

Forré, Patrick (2011) On the kernel of the reciprocity map of varieties over local fields. PhD, Universität Regensburg.

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Date of publication of this fulltext: 05 Aug 2011 08:10

Abstract (English)

This thesis is about higher dimensional class field theory of varieties over local and finite fields. Their abelianized étale fundamental group is compared with an attached class group via the reciprocity map, like in the classical case of a local or global field. The main results in this thesis are about the structure of the kernel of their reciprocity maps and criteria for the vanishing of it, resp..

Translation of the abstract (German)

Diese Dissertation handelt von der höherdimensionalen Klassenkörpertheorie von Varietäten über lokalen und endlichen Körpern. Ihre abelisierte étale Fundamantalgruppe wird wie im klassichen Fall von lokalen oder globalen Körpern via einer Reziprozitätsabbildung mit der zugehörigen Klassengruppe verglichen. Die Hauptresultate in dieser Arbeit betreffen die Struktur des Kerns der Reziprozitätsabbildung bzw. Kriterien für ihr verschwinden.

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Item type:Thesis of the University of Regensburg (PhD)
Date:5 August 2011
Referee:Prof. Dr. Uwe Jannsen and Prof. Dr. Alexander Schmidt
Date of exam:28 July 2011
Institutions:Mathematics > Prof. Dr. Uwe Jannsen
Keywords:higher dimensional class field theory, reciprocity map, abelianized fundamental group, étale homology theory, Kato homology groups, varieties over finite fields, varieties over local fields
Dewey Decimal Classification:500 Science > 510 Mathematics
Refereed:Yes, this version has been refereed
Created at the University of Regensburg:Yes
Item ID:21639
Owner only: item control page


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