On the algebraic fundamental group of smooth varieties in characteristic
Authors:
Hélène Esnault and Amit Hogadi
Journal:
Trans. Amer. Math. Soc. 364 (2012), 2429-2442
MSC (2010):
Primary 14F35
DOI:
https://doi.org/10.1090/S0002-9947-2012-05470-5
Published electronically:
January 17, 2012
MathSciNet review:
2888213
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We define an analog in characteristic of the proalgebraic completion of the topological fundamental group of a complex manifold.
- 1. P. Deligne, Catégories tannakiennes, The Grothendieck Festschrift, Vol. II, Progr. Math., vol. 87, Birkhäuser Boston, Boston, MA, 1990, pp. 111–195 (French). MR 1106898
- 2. Deligne, P., Milne, J.: Tannakian Categories, Lecture Notes in Mathematics 900, 101-228, Springer-Verlag, 1982.
- 3. João Pedro Pinto dos Santos, Fundamental group schemes for stratified sheaves, J. Algebra 317 (2007), no. 2, 691–713. MR 2362937, https://doi.org/10.1016/j.jalgebra.2007.03.005
- 4. dos Santos, J.-P.: Fundamental group-schemes in positive characteristic, Reports Oberwolfach, 2007.
- 5. Hélène Esnault, Phùng Hô Hai, and Xiaotao Sun, On Nori’s fundamental group scheme, Geometry and dynamics of groups and spaces, Progr. Math., vol. 265, Birkhäuser, Basel, 2008, pp. 377–398. MR 2402410, https://doi.org/10.1007/978-3-7643-8608-5_8
- 6. Hélène Esnault and Phùng Hô Hai, The fundamental groupoid scheme and applications, Ann. Inst. Fourier (Grenoble) 58 (2008), no. 7, 2381–2412 (English, with English and French summaries). MR 2498355
- 7.
Esnault, H., Mehta, V.: Simply connected projective manifolds in characteristic
have no nontrivial stratified bundles, preprint 2009, 12 pages.
- 8. van der Geer, G., Moonen, B.: Abelian varieties, http://staff.science.uva.nl/bmoonen/boek/BookAV.html.
- 9. D. Gieseker, Flat vector bundles and the fundamental group in non-zero characteristics, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 2 (1975), no. 1, 1–31. MR 382271
- 10. Madhav V. Nori, The fundamental group-scheme, Proc. Indian Acad. Sci. Math. Sci. 91 (1982), no. 2, 73–122. MR 682517, https://doi.org/10.1007/BF02967978
Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 14F35
Retrieve articles in all journals with MSC (2010): 14F35
Additional Information
Hélène Esnault
Affiliation:
Department of Mathematics, Universität Duisburg-Essen, 45117 Essen, Germany
Email:
esnault@uni-due.de
Amit Hogadi
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
Email:
amit@math.tifr.res.in
DOI:
https://doi.org/10.1090/S0002-9947-2012-05470-5
Received by editor(s):
April 11, 2010
Published electronically:
January 17, 2012
Additional Notes:
The author was supported by the DFG Leibniz Preis, the SFB/TR45, and the ERC Advanced Grant 226257
Article copyright:
© Copyright 2012
American Mathematical Society