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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Frobenius-unstable bundles and $ p$-curvature


Author: Brian Osserman
Journal: Trans. Amer. Math. Soc. 360 (2008), 273-305
MSC (2000): Primary 14H60
Published electronically: May 17, 2007
MathSciNet review: 2342003
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Abstract: We use the theory of $ p$-curvature of connections to analyze stable vector bundles of rank 2 on curves of genus 2 which pull back to unstable bundles under the Frobenius morphism. We take two approaches, first using explicit formulas for $ p$-curvature to analyze low-characteristic cases, and then using degeneration techniques to obtain an answer for a general curve by degenerating to an irreducible rational nodal curve, and applying the results of additional works by the author. We also apply our explicit formulas to give a new description of the strata of curves of genus 2 of different $ p$-rank.


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Additional Information

Brian Osserman
Affiliation: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720-3840

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04218-3
PII: S 0002-9947(07)04218-3
Received by editor(s): September 17, 2004
Received by editor(s) in revised form: November 11, 2005
Published electronically: May 17, 2007
Additional Notes: This paper was partially supported by fellowships from the National Science Foundation and Japan Society for the Promotion of Science.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.