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Transcendence and linear relations of $1$-periods
- Publication Year :
- 2018
-
Abstract
- We study four fundamental questions about $1$-periods and give complete answers. 1) We give a necessary and sufficient for a period integral to be transcendental. 2) We give a qualitative description of all $\overline{\mathbf{Q}}$-linear relations between $1$-periods, establishing Kontsevich's period conjecture in this case. 3) Periods may vanish and we determine all cases when this happens. 4) For a fixed $1$-motive, we derive a general formula for the dimension of its space of periods in the spirit of Baker's theorem.<br />Comment: This is the final draft and very close to the published version of the monograph, but not identical. In particular layout and page numbers do not agree. To appear: Cambridge Tracts in Mathematics 227, Cambridge University Press, May 2022. Copyright Annette Huber and Gisbert W\"ustholz
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1805.10104
- Document Type :
- Working Paper