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Wild ramification of schemes via curves, the rank 1 case (with applications to higher class field theory)
Barrientos, Ivan (2014) Wild ramification of schemes via curves, the rank 1 case (with applications to higher class field theory). PhD, Universität Regensburg.Date of publication of this fulltext: 12 Sep 2014 14:07
Thesis of the University of Regensburg
DOI to cite this document: 10.5283/epub.30739
Abstract (English)
We prove that in rank 1, the Abbes-Saito log conductor is determined by its restriction to curves. This result is essentially established by analyzing Artin-Schreier-Witt extensions. Consequently, we confirm an expectation of H. Esnault and M. Kerz. We also conjecture that this result holds in arbitrary finite rank. As an application, we translate recent results in higher class field theory of M. Kerz and S. Saito to the log-ramification context.
Translation of the abstract (German)
Wir beweisen, dass der Abbes-Saito-Log Führer im Fall der Rang 1 durch seine Einschränkung auf Kurven beschrieben ist. Dieses Ergebnis ist durch eine Analyse der Schreier-Witt Erweiterungen geprüft. Somit bestätigen wir eine Erwartung von H. Esnault und M. Kerz. Außerdem vermuten wir, dass dieses Resultat für einen beliebigen endlichen Rang gilt. Als Anwendung übersetzen wir die Arbeit von M. Kerz und S. Saito
über höhere Klassenkörpertheorie auf den Log-Verzweigung Kontext.
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Details
| Item type | Thesis of the University of Regensburg (PhD) |
| Open Access Type: | Primary Publication |
|---|---|
| Date | 12 September 2014 |
| Referee | Prof. Dr. Moritz Kerz |
| Date of exam | 18 July 2014 |
| Institutions | Mathematics > Prof. Dr. Moritz Kerz |
| Keywords | wild ramification, conductor, higher class field theory |
| Dewey Decimal Classification | 500 Science > 510 Mathematics |
| Status | Published |
| Refereed | Yes, this version has been refereed |
| Created at the University of Regensburg | Yes |
| URN of the UB Regensburg | urn:nbn:de:bvb:355-epub-307397 |
| Item ID | 30739 |
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