7 dec 2017 -- 16:00
Aula Fermi, SNS, Pisa
Abstract.
Calabi-Yau (CY) algebraic varieties are generalizations of elliptic curves and K3 surfaces. CY 3-folds arise in some models of string theory, and so have been studied intensively by mathematicians and physicists. In two beautiful papers, Claire Voisin studied the group of algebraic cycles of codimension two on a non-rigid CY 3-fold X over the complex numbers that are homologically equivalent to zero, but not algebraically equivalent to zero. Her main result is that on a general deformation of X, this group is infinitely generated, and the proof uses Hodge theoretic methods. In this talk, we will discuss an analogue of her work over p-adic fields using p-adic methods. All terms in this abstract will be defined.