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Mathematics > Algebraic Geometry

arXiv:1805.07121 (math)
[Submitted on 18 May 2018 (v1), last revised 4 Nov 2019 (this version, v2)]

Title:Motivic periods and Grothendieck arithmetic invariants

Authors:F. Andreatta, L. Barbieri-Viale, A. Bertapelle
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Abstract:We construct a period regulator for motivic cohomology of an algebraic scheme over a subfield of the complex numbers. For the field of algebraic numbers we formulate a period conjecture for motivic cohomology by saying that this period regulator is surjective. Showing that a suitable Betti--de Rham realization of 1-motives is fully faithful we can verify this period conjecture in several cases. The divisibility properties of motivic cohomology imply that our conjecture is a neat generalization of the classical Grothendieck period conjecture for algebraic cycles on smooth and proper schemes. These divisibility properties are treated in an appendix by B. Kahn (extending previous work of Bloch and Colliot-Thélène--Raskind).
Comments: Appendix by B. Kahn added. Revised version to appear on Adv. Math
Subjects: Algebraic Geometry (math.AG); K-Theory and Homology (math.KT); Number Theory (math.NT)
MSC classes: 14F42, 14F40, 19E15, 14C30, 14L15
Cite as: arXiv:1805.07121 [math.AG]
  (or arXiv:1805.07121v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.07121
Journal reference: Advances in Mathematics Vol. 359 (2020) 106880
Related DOI: https://doi.org/10.1016/j.aim.2019.106880

Submission history

From: L. Barbieri-Viale [view email]
[v1] Fri, 18 May 2018 10:06:44 UTC (36 KB)
[v2] Mon, 4 Nov 2019 16:56:18 UTC (44 KB)
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