Gauss-Manin stratification and stratified fundamental group schemes

We defined the Gau\ss-Manin stratification of a stratified bundle with respect to a smooth morphism and use it to study the homotopy sequence of stratified fundamental group schemes.Comment: 14 pages, the proof of Prop. 2.8 is corrected. To appear in Annales de l'Institut Fourie

Packets in Grothendieck's Section Conjecture

Using the identification of sections of the Galois group of the ground field into the arithmetic fundamental group with neutral fiber functors of the category of finite connections, we define the "packets" in Grothendieck's section conjecture and show their properties predicted by him.Comment: 22 pages (no changes on the mathematical content but the exposition has been shortened

Connections on trivial vector bundles over projective schemes

Over a smooth and proper complex scheme, the differential Galois group of an integrable connection may be obtained as the closure of the transcendental monodromy representation. In this paper, we employ a completely algebraic variation of this idea by restricting attention to connections on trivial vector bundles and replacing the fundamental group by a certain Lie algebra constructed from the regular forms. In more detail, we show that the differential Galois group is a certain ``closure'' of the aforementioned Lie algebra. This is then applied to construct connections on curves with prescribed differential Galois group.Comment: A reader pointed out an error; we have removed the results concerning applications to the connections on the projective lin