S-unit equation and Chabauty
Friday, 8.1.21, 10:30-11:30, SR 404
Algebraic cycles and refined unramified cohomology
Friday, 15.1.21, 10:30-11:30, SR 404
We introduce refined unramified cohomology groups. This notion allows us to give in arbitrary degree a cohomological interpretation of the failure of integral Hodge- or Tate-type conjectures, of l-adic Griffiths groups, and of the subgroup of the Griffiths group that consists of torsion classes with trivial transcendental Abel--Jacobi invariant. Our approach simplifies and generalizes to cycles of arbitrary codimension previous results of Bloch--Ogus, Colliot-Thélène--Voisin, Voisin, and Ma that concerned cycles of codimension two or three. As an application, we give for any i>2 the first example of a uniruled smooth complex projective variety for which the integral Hodge conjecture fails for codimension i-cycles in a way that cannot be explained by the failure on any lower-dimensional variety.
Irregular fibrations and derived categories
Friday, 22.1.21, 10:30-11:30, SR 404
In this seminar I will show that an equivalence of derived categories of sheaves of smooth projective varieties preserves some specific classes of fibrations over varieties of maximal Albanese dimension. These types of fibrations, called chi-positive higher irrational pencils, can be thought as an extension to higher-dimension of the notion of a irrational pencil over a smooth curve of genus greater or equal to two. This is a joint work with F. Caucci and G. Pareschi.
Cone structures and parabolic geometries
Friday, 29.1.21, 10:30-11:30, SR 404