Graf, Philipp (2016) Polylogarithms for GL₂ over totally real fields. PhD, Universität Regensburg.
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Abstract (English)
We generate the Eisenstein cohomology of Hilbert-Blumenthal varieties by classes coming from a topological constuction called the polylogarithm. This gives an alternative proof of Günter Harder's theorem that the Eisenstein operator on cohomology is rational. Moreover, integrality results for special values of L-functions over totally real fields are proved along the way.
Translation of the abstract (German)
Wir erzeugen die Eisenstein Kohomologie von Hilbert-Blumenthal Varietäten durch Klassen, die von einer geometrischen Konstruktion, dem Polylogarithmus, herkommen. Dies liefert einen alternativen Beweis für Günter Harder's Theorem, dass der Eisenstein Operator auf der Kohomologie rational ist. Darüberhinaus werden Ganzheitsaussagen für spezielle Werte von L-Funktionen über total reellen Zahlkörpern bewiesen.
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| Item type: | Thesis of the University of Regensburg (PhD) |
|---|---|
| Date: | 21 April 2016 |
| Referee: | Prof. Dr. Guido Kings |
| Date of exam: | 4 February 2016 |
| Institutions: | Mathematics > Prof. Dr. Guido Kings |
| Keywords: | Eisenstein Kohomologie, Eisenstein Klassen, Eisenstein Reihen, Polylogarithmus, Hilbert-Blumenthal Varietät Eisenstein cohomology, Eisenstein series, polylogarithm, Hilbert-Blumenthal variety |
| Dewey Decimal Classification: | 500 Science > 510 Mathematics |
| Status: | Published |
| Refereed: | Yes, this version has been refereed |
| Created at the University of Regensburg: | Yes |
| Item ID: | 33593 |
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