Holmstrom Fundamental groups in algebraic geometry

Motivic fundamental group? See various things of Kim.

http://londonnumbertheory.wordpress.com/2010/05/10/fundamental-groups-are-not-galois-groups/

Fundamental groups, and also Grothendieck’s section conjecture - see Kim Cambridge lecture July 09

arXiv:0908.0498 On the homotopy exact sequence for Nori’s fundamental group from arXiv Front: math.AG by Hélène Esnault, Phùng Hô Hai, Eckart Viehweg Unlike Grothendieck’s étale fundamental group, Nori’s fundamental group does not fulfill the homotopy exact sequence in general. We give necessary and sufficient conditions which force exactness of the sequence.

arXiv:1003.3599 On the algebraic fundamental group of smooth varieties in characteristic $p>0$ from arXiv Front: math.AG by Hélène Esnault, Amit Hogadi We define an analog in characteristic $p>0$ of the proalgebraic completion of the topological fundamental group of a complex manifold.

nLab page on Fundamental groups in algebraic geometry