Séminaire de Mathématique

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

## by Prof. Nobuo TSUZUKI (Tohoku University)

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 P1 Z[1/2]
{0, 1, ¥}, which is a projective smooth model of the affine scheme [ w2 = x1·s xn(1-x1)·s(1-xn)(1 - l x1·s xn), ] such that the generalized hypergeometric series n+1Fn(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.
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