# On the homotopy exact sequence for the algebraic fundamental group

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Valentina Di Proietto

created by risa on 01 Mar 2015

18 mar 2015
-- 14:30

Aula di Consiglio, Dip. Matematica, Università "La Sapienza", Roma

**Abstract.**

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.