Gauss-Manin stratification and stratified fundamental group schemes
[Stratification de Gauss-Manin et groupes fondamentaux stratifiés]
Phùng, Hô Hai
Annales de l'Institut Fourier, Tome 63 (2013), p. 2267-2285 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

On définit la stratification de Gauss-Manin d’un fibré stratifié relativement à un morphisme lisse et on l’utilise pour étudier la suite d’homotopie des groupes fondamentaux stratifiés.

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.

Publié le : 2013-01-01
DOI : https://doi.org/10.5802/aif.2829
Classification:  14F05,  14F35,  14L17
Mots clés: Fibré stratifié, Stratification de Gauss-Manin, Suite d’homotopie 
@article{AIF_2013__63_6_2267_0,
     author = {Ph\`ung, H\^o Hai},
     title = {Gauss-Manin stratification and stratified fundamental group schemes},
     journal = {Annales de l'Institut Fourier},
     volume = {63},
     year = {2013},
     pages = {2267-2285},
     doi = {10.5802/aif.2829},
     zbl = {1298.14022},
     mrnumber = {3237447},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2013__63_6_2267_0}
}

Phùng, Hô Hai. Gauss-Manin stratification and stratified fundamental group schemes. Annales de l'Institut Fourier, Tome 63 (2013) pp. 2267-2285. doi : 10.5802/aif.2829. http://gdmltest.u-ga.fr/item/AIF_2013__63_6_2267_0/

[1] Berthelot, P.; Ogus, A. Notes on crystalline cohomology, Princeton Univ. Press (1978) | MR 491705 | Zbl 0383.14010

[2] Deligne, P.; Milne, J. S. Tannakian Categories, Hodge Cycles, Motives, and Shimura Varieties, Springer-Verlag (Lectures Notes in Mathematics) Tome 900 (1981), pp. 101-228 | Zbl 0477.14004

[3] Esnault, H.And; Mehta, V. Simply connected projective manifolds incharacteristic p>0 have no nontrivial stratified bundles, Inventiones Mathematicae, Tome 181 (2010), pp. 449-465 | Article | MR 2660450 | Zbl 1203.14029

[4] Esnault, P. H. H.And Hai The Gauss-Manin connection and Tannaka duality, Int. Math. Res. Not., Art. ID 93978 (2006), pp. 1-35 | MR 2211153 | Zbl 1105.14012

[5] Esnault, P. H. H.And Hai; Sun, X. On Nori’s Fundamental Group Scheme, Progress in Mathematics, Tome 265 (2007), pp. 377-398 | Article | MR 2402410 | Zbl 1137.14035

[6] Gieseker, D. Flat vector bundles, Annali della Scuola Normale Superiore di Pisa (1975) no. 1, pp. 1-31 | Numdam | MR 382271 | Zbl 0322.14009

[7] Grothendieck, A.; Dieudonné, J. Éléments de Géométrie Algébrique III, (EGA 3), Publication Math. IHES Tome 17 (1963)

[8] Grothendieck, A.; Dieudonné, J. Éléments de Géométrie Algébrique IV (EGA 4), Publication Math. IHES Tome 32 (1967)

[9] Hartshorne, R. Algebraic geometry, Springer (1977) | MR 463157 | Zbl 0531.14001

[10] Katz, N. Nilpotent connections and the monodromy theorem: applications of a result of Turrittin, Publ. Math. IHES, Tome 39 (1970), pp. 175-232 | Article | Numdam | MR 291177 | Zbl 0221.14007

[11] Ogus, A. Cohomology of the infinitesimal site, Annales scientifiques E.N.S., Tome 8 (1975) no. 3, pp. 295-318 | Numdam | MR 422280 | Zbl 0337.14018

[12] Dos Santos, J. Fundamental group schemes for stratified sheaves, Journal of Algebra, Tome 317 (2007), pp. 691-713 | Article | MR 2362937 | Zbl 1130.14032

[13] Dos Santos, J. The behaviour of the differential Galois group on the generic and special fibres: A Tannakian approach, J. reine angew. Math., Tome 637 (2009), pp. 63-98 | MR 2599082 | Zbl 1242.12005