On Birch-Swinnerton-Dyer volumes of hypergeometric Calabi-Yau motives

par Vasily Golyshev

jeudi 15 déc. 2022, 14:00 → 15:00 Europe/Paris

In a program to study Picard-Fuchs differential equations controlling regulators in pencils of algebraic varieties, we investigate hypergeometric variations of rank 4 weight 3 Calabi--Yau motives.  We write down explicit hypergeometric expressions for their Birch--Swinnerton-Dyer volumes, and compare them numerically to the first derivative of the $L$--functions of these motives at the central argument $s=2$ in analytic rank 1 cases.