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

Pauly, Christian

doi:10.1090/S0002-9939-07-08805-3

A smooth counterexample to Nori’s conjecture on the fundamental group scheme
HTML articles powered by AMS MathViewer

by Christian Pauly

Proc. Amer. Math. Soc. 135 (2007), 2707-2711

DOI: https://doi.org/10.1090/S0002-9939-07-08805-3

Published electronically: May 2, 2007

PDF | Request permission

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

H. Lange, C. Pauly: On Frobenius-destabilized rank-2 vector bundles over curves, arxiv.math.AG/0309456
Y. Laszlo and C. Pauly, The action of the Frobenius maps on rank $2$ vector bundles in characteristic $2$, J. Algebraic Geom. 11 (2002), no. 2, 219–243. MR 1874113, DOI 10.1090/S1056-3911-01-00310-1
Yves Laszlo and Christian Pauly, The Frobenius map, rank 2 vector bundles and Kummer’s quartic surface in characteristic 2 and 3, Adv. Math. 185 (2004), no. 2, 246–269. MR 2060469, DOI 10.1016/S0001-8708(03)00211-1
J. Le Potier, Lectures on vector bundles, Cambridge Studies in Advanced Mathematics, vol. 54, Cambridge University Press, Cambridge, 1997. Translated by A. Maciocia. MR 1428426
V. B. Mehta and S. Subramanian, On the fundamental group scheme, Invent. Math. 148 (2002), no. 1, 143–150. MR 1892846, DOI 10.1007/s002220100191
Madhav V. Nori, The fundamental group-scheme, Proc. Indian Acad. Sci. Math. Sci. 91 (1982), no. 2, 73–122. MR 682517, DOI 10.1007/BF02967978