238 research outputs found
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
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