Some remarks concerning the Grothendieck Period Conjecture
Abstract
We discuss various results and questions around the Grothendieck period conjecture, which is a counterpart, concerning the de Rham-Betti realization of algebraic varieties over number fields, of the classical conjectures of Hodge and Tate. These results give new evidence towards the conjectures of Grothendieck and Kontsevich-Zagier concerning transcendence properties of the torsors of periods of varieties over number fields. We notably establish that the Grothendieck period conjecture holds in degree 1 for products of curves, of abelian varieties, and of K3 surfaces, and that it holds in degree 2 for smooth cubic fourfolds.
Keywords
Cite
@article{arxiv.1307.1045,
title = {Some remarks concerning the Grothendieck Period Conjecture},
author = {Jean-Benoît Bost and François Charles},
journal= {arXiv preprint arXiv:1307.1045},
year = {2014}
}
Comments
Section 2 substantially revised, notably to correct the Proposition 2.12 of the first version and to clarify the fields of definitions of the algebraic groups underlying the diverse torsors of periods. In other Sections, mainly expository modifications