Transcendence and linear relations of $1$-periods

Annette Huber; Gisbert Wüstholz

Transcendence and linear relations of $1$-periods

Number Theory 2022-04-22 v8 Algebraic Geometry

Authors: Annette Huber , Gisbert Wüstholz

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.

Keywords

1-periods transcendence linear relations period conjecture baker's theorem 1-motives

Cite

@article{arxiv.1805.10104,
  title  = {Transcendence and linear relations of $1$-periods},
  author = {Annette Huber and Gisbert Wüstholz},
  journal= {arXiv preprint arXiv:1805.10104},
  year   = {2022}
}

Comments

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

Transcendence and linear relations of $1$-periods

Abstract

Keywords

Cite

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