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The de Rham realization of the elliptic polylogarithm in families
Thesis of the University of Regensburg
Scheider, René Achim (2014) The de Rham realization of the elliptic polylogarithm in families. PhD, Universität Regensburg.DOI to cite this document: 10.5283/epub.30413
Abstract (English)
We give a geometric construction of the logarithm sheaves on an abelian scheme in terms of the universal vectorial extension and the Poincaré bundle.
Building on this approach we then develop an explicit description for the de Rham realization of the polylogarithm on the universal elliptic curve with level N structure and express its specialization along torsion sections by certain algebraic Eisenstein series.
Translation of the abstract (German)
Wir geben eine geometrische Konstruktion der Logarithmusgarben auf einem abelschen Schema in Termen der universellen Vektorerweiterung und des Poincaré Bündels.
Auf diesem Zugang aufbauend entwickeln wir dann eine explizite Beschreibung für die de Rham Realisierung des Polylogarithmus auf der universellen elliptischen Kurve mit Level N Struktur und drücken seine Spezialisierung längs Torsionsschnitten durch bestimmte algebraische Eisensteinreihen aus.
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Details
| Item type | Thesis of the University of Regensburg (PhD) |
| Open Access Type | Primary Publication |
| Date | 16 July 2014 |
| Date of publication | 16 Jul 2014 15:27 |
| Referee | Prof. Dr. Guido Kings |
| Date of exam | 13 June 2014 |
| Institutions | Mathematics > Prof. Dr. Guido Kings |
| Keywords | de Rham realization of the polylogarithm, universal vectorial extension, Poincaré bundle, elliptic curves |
| 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-304133 |
| Item ID | 30413 |
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