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A smooth counterexample to Nori's conjecture on the fundamental group scheme

Author(s): Christian Pauly
Journal: Proc. Amer. Math. Soc. 135 (2007), 2707-2711.
MSC (2000): Primary 14H60, 14D20; Secondary 14H30
Posted: May 2, 2007
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Abstract: We show that Nori's fundamental group scheme $ \pi(X,x)$ does not base change correctly under extension of the base field for certain smooth projective ordinary curves $ X$ of genus $ 2$ defined over a field of characteristic $ 2$.

References:

[LaP]
H. Lange, C. Pauly: On Frobenius-destabilized rank-2 vector bundles over curves, arxiv.math.AG/0309456

[LP1]
Y. Laszlo, C. Pauly: The action of the Frobenius maps on rank $ 2$ vector bundles in characteristic $ 2$, J. Alg. Geometry 11 (2002), 219-243 MR 1874113 (2003a:14051)

[LP2]
Y. Laszlo, C. Pauly: The Frobenius map, rank $ 2$ vector bundles and Kummer's quartic surface in characteristic $ 2$ and $ 3$, Adv. Math. 185, No. 2 (2004), 246-269 MR 2060469 (2005d:14049)

[LeP]
J. Le Potier: Lectures on vector bundles, Cambridge Studies in Advanced Mathematics 54, Cambridge University Press, 1997 MR 1428426 (98a:14019)

[MS]
V.B. Mehta, S. Subramanian: On the fundamental group scheme, Invent. Math. 148 (2002), 143-150 MR 1892846 (2004c:14089)

[N]
M.V. Nori, The fundamental group scheme, Proc. Indian Acad. Sci. (Math. Sci.) 91 (1982), 78-122 MR 0682517 (85g:14019)

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Additional Information:

Christian Pauly
Affiliation: Département de Mathématiques, Université de Montpellier II - Case Courrier 051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France
Email: pauly@math.univ-montp2.fr

DOI: 10.1090/S0002-9939-07-08805-3
PII: S 0002-9939(07)08805-3
Received by editor(s): January 10, 2006
Received by editor(s) in revised form: May 18, 2006
Posted: May 2, 2007
Communicated by: Ted Chinburg
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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