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Mathematics > Number Theory

arXiv:1805.10104 (math)
[Submitted on 25 May 2018 (v1), last revised 21 Apr 2022 (this version, v8)]

Title:Transcendence and linear relations of $1$-periods

Authors:Annette Huber, Gisbert Wüstholz
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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.
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 Wüstholz
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
MSC classes: 11J81, 14F42, 14C15, 14C30
Cite as: arXiv:1805.10104 [math.NT]
  (or arXiv:1805.10104v8 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1805.10104

Submission history

From: Annette Huber [view email]
[v1] Fri, 25 May 2018 12:29:43 UTC (49 KB)
[v2] Wed, 8 Aug 2018 11:09:56 UTC (58 KB)
[v3] Thu, 22 Nov 2018 13:13:16 UTC (63 KB)
[v4] Wed, 3 Apr 2019 10:40:12 UTC (72 KB)
[v5] Mon, 4 Nov 2019 08:06:36 UTC (87 KB)
[v6] Fri, 4 Jun 2021 11:29:43 UTC (133 KB)
[v7] Mon, 16 Aug 2021 12:05:46 UTC (154 KB)
[v8] Thu, 21 Apr 2022 07:58:16 UTC (156 KB)
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