18 mar 2015 -- 14:30
Aula di Consiglio, Dip. Matematica, Università "La Sapienza", Roma
There is a strong link between the fundamental group of a variety and the linear differential equations we can define on it. The definition of the fundamental group given in terms of homotopy classes of loops does not generalize easily to algebraic varieties defined over an arbitrary field. But exploiting this link we can give an other definition that makes sense in very general contexts: it is called the algebraic fundamental group. We prove the homotopy exact sequence for the algebraic fundamental group for a fibration with singularities with normal crossing. This is a joint work with Atsushi Shiho.