Valentina Di Proietto


Title: On the homotopy exact sequence for the algebraic fundamental group


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 and we explain how this gives 
a monodromy action on the algebraic fundamental group.  This is a joint work with Atsushi Shiho.