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.
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Submitted on : Wednesday, July 10, 2013 - 2:56:35 PM
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Jean-Benoît Bost, François Charles. Some remarks concerning the Grothendieck Period Conjecture. Journal für die reine und angewandte Mathematik, Walter de Gruyter, 2016, pp.175-208. ⟨10.1515/crelle-2014-0025⟩. ⟨hal-00843112⟩



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