Séminaire de Mathématique
# On integral cohomologies for an arithmetic family of hypergeometric Calabi-Yau

→
Europe/Paris

Amphithéâtre Léon Motchane (Institut des Hautes Etudes Scientifiques)
### Amphithéâtre Léon Motchane

#### Institut des Hautes Etudes Scientifiques

Bois-Marie
35, route de Chartres
91440 Bures-sur-Yvette

Description

We constructed a family of Calabi-Yau varieties over the l-line P^{1} _{ Z[1/2]}

{0, 1, ¥}, which is a projective smooth model of the affine scheme [ w^{2}
= x_{1}·s x_{n}(1-x_{1})·s(1-x_{n})(1 - l x_{1}·s x_{n}), ]
such that the generalized hypergeometric series _{n+1}F_{n}(1/2, ·s,1/2; 1, ·s, 1; l) appear in the middle cohomology as a period function. In this talk we recall the construction of the family and how to calculate various cohomologies (Betti, de Rham, etale, and crystalline), discuss torsion freeness, up to 2-torsions, of integral cohomologies, and prove the integral version of degeneration of the Hodge to de Rham spectral sequence.

{0, 1, ¥}, which is a projective smooth model of the affine scheme [ w

Contact