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

par Prof. Nobuo TSUZUKI (Tohoku University)

mercredi 12 mars 2014, 16:30 → 17:30 Europe/Paris

Amphithéâtre Léon Motchane (Institut des Hautes Etudes Scientifiques)

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 x_n(1-x₁)·s(1-x_n)(1 - l x₁·s x_n), ] such that the generalized hypergeometric series _n+1F_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.

Transparents ResuTSUZUKI.pdf (Protégé)