logo ANNALES DE L'INSTITUT FOURIER

With cedram.org
Table of contents for this issue | Previous article | Next article
Hô Hai Phùng
Gauss-Manin stratification and stratified fundamental group schemes
(Stratification de Gauss-Manin et groupes fondamentaux stratifiés)
Annales de l'institut Fourier, 63 no. 6 (2013), p. 2267-2285, doi: 10.5802/aif.2829
Article PDF | Reviews MR 3237447 | Zbl 1298.14022
Class. Math.: 14F05, 14F35, 14L17
Keywords: Stratified bundle, Gauss-Manin stratification, homotopy sequence

Résumé - Abstract

We define the zero-th Gauss-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.

Bibliography

[1] P. Berthelot & A. Ogus, Notes on crystalline cohomology, Princeton Univ. Press, 1978  MR 491705 |  Zbl 0383.14010
[2] P. Deligne & J. S. Milne, Tannakian Categories, Hodge Cycles, Motives, and Shimura Varieties, Lectures Notes in Mathematics 900, Springer-Verlag, 1981, p. 101-228  Zbl 0477.14004
[3] H.and Esnault & V. Mehta, “Simply connected projective manifolds incharacteristic $p > 0$ have no nontrivial stratified bundles”, Inventiones Mathematicae 181 (2010), p. 449-465 Article |  MR 2660450 |  Zbl 1203.14029
[4] P. H. Esnault, “The Gauss-Manin connection and Tannaka duality”, Int. Math. Res. Not., Art. ID 93978 (2006), p. 1-35  MR 2211153 |  Zbl 1105.14012
[5] P. H. Esnault & X. Sun, “On Nori’s Fundamental Group Scheme”, Progress in Mathematics 265 (2007), p. 377-398 Article |  MR 2402410 |  Zbl 1137.14035
[6] D. Gieseker, “Flat vector bundles”, Annali della Scuola Normale Superiore di Pisa (1975) no. 1, p. 1-31 Numdam |  MR 382271 |  Zbl 0322.14009
[7] A. Grothendieck & J. Dieudonné, Éléments de Géométrie Algébrique III, (EGA 3) 17, Publication Math. IHES, 1963
[8] A. Grothendieck & J. Dieudonné, Éléments de Géométrie Algébrique IV (EGA 4) 32, Publication Math. IHES, 1967
[9] R. Hartshorne, Algebraic geometry, Springer, 1977  MR 463157 |  Zbl 0531.14001
[10] N. Katz, “Nilpotent connections and the monodromy theorem: applications of a result of Turrittin”, Publ. Math. IHES 39 (1970), p. 175-232 Numdam |  MR 291177 |  Zbl 0221.14007
[11] A. Ogus, “Cohomology of the infinitesimal site”, Annales scientifiques E.N.S. 8 (1975) no. 3, p. 295-318 Numdam |  MR 422280 |  Zbl 0337.14018
[12] J. dos Santos, “Fundamental group schemes for stratified sheaves”, Journal of Algebra 317 (2007), p. 691-713 Article |  MR 2362937 |  Zbl 1130.14032
[13] J. dos Santos, “The behaviour of the differential Galois group on the generic and special fibres: A Tannakian approach”, J. reine angew. Math. 637 (2009), p. 63-98  MR 2599082 |  Zbl 1242.12005
top