A remark on Frobenius descent for vector bundles
Holger Brenner and Almar Kaid
Source: Michigan Math. J. Volume 57 (2008), 63-69.
Primary Subjects: 14H60
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.mmj/1220879397
Digital Object Identifier: doi:10.1307/mmj/1220879397
Mathematical Reviews number (MathSciNet):
MR2492441
Zentralblatt MATH identifier:
05604520
References
M. F. Atiyah, Vector bundles over an elliptic curve, Proc. London Math. Soc. (3) 7 (1957), 414--452.
Mathematical Reviews (MathSciNet):
MR131423
Digital Object Identifier: doi:10.1112/plms/s3-7.1.414
H. Brenner, Computing the tight closure in dimension two, Math. Comp. 74 (2005), 1495--1518.
Mathematical Reviews (MathSciNet):
MR2137014
Digital Object Identifier: doi:10.1090/S0025-5718-05-01730-8
------, On a problem of Miyaoka, Number fields and function fields: Two parallel worlds (B. Moonen, R. Schoof, G. van derGeer, eds.), Progr. Math., 239, pp. 51--59, Birkhäuser, Boston, 2005.
Mathematical Reviews (MathSciNet):
MR2176585
Digital Object Identifier: doi:10.1007/0-8176-4447-4_3
------, The rationality of the Hilbert--Kunz multiplicity in graded dimension two, Math. Ann. 334 (2006), 91--110.
Mathematical Reviews (MathSciNet):
MR2208950
Digital Object Identifier: doi:10.1007/s00208-005-0703-x
H. Brenner and A. Kaid, On deep Frobenius descent and flat bundles, preprint, 2007, arXiv:0712.1794.
Mathematical Reviews (MathSciNet):
MR2470387
K. Joshi, Some remarks on vector bundles, preprint, 2007, $\langle $http://math.arizona.edu/kirti/homepage$\rangle .$
N. M. Katz, Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin, Inst. Hautes Études Sci. Publ. Math. 39 (1970), 175--232.
Mathematical Reviews (MathSciNet):
MR291177
Digital Object Identifier: doi:10.1007/BF02684688
H. Lange and C. Pauly, On Frobenius-destabilized rank-2 vector bundles over curves, Comment. Math. Helv. 83 (2008), 179--209.
Mathematical Reviews (MathSciNet):
MR2365412
A. Langer, Semistable sheaves in positive characteristic, Ann. of Math. (2) 159 (2004), 251--276.
Mathematical Reviews (MathSciNet):
MR2051393
Digital Object Identifier: doi:10.4007/annals.2004.159.251
V. B. Mehta and A. Ramanathan, Homogeneous bundles in characteristic $p,$ Algebraic geometry: Open problems (Ravello, 1982), Lecture Notes in Math., 997, pp. 315--320, Springer-Verlag, Berlin, 1982.
Mathematical Reviews (MathSciNet):
MR714755
Zentralblatt MATH:
0532.14007
Digital Object Identifier: doi:10.1007/BFb0061650
Y. Miyaoka, The Chern class and Kodaira dimension of a minimal variety, Algebraic geometry (Sendai, 1985), Adv. Stud. Pure Math., 10, pp. 449--476, North-Holland, Amsterdam, 1987.
Mathematical Reviews (MathSciNet):
MR946247
Zentralblatt MATH:
0648.14006
P. Monsky, The Hilbert--Kunz function, Math. Ann. 263 (1983), 43--49.
Mathematical Reviews (MathSciNet):
MR697329
Digital Object Identifier: doi:10.1007/BF01457082
------, The Hilbert--Kunz multiplicity of an irreducible trinomial, J. Algebra 304 (2006), 1101--1107.
Mathematical Reviews (MathSciNet):
MR2265506
Digital Object Identifier: doi:10.1016/j.jalgebra.2005.12.028
J. P. Serre, Cours d'arithmétique, Le mathématicien, vol. 2, Presses Universitaires de France, Paris, 1970.
Mathematical Reviews (MathSciNet):
MR255476
N. I. Shepherd-Barron, Semi-stability and reduction $\text\it mod~p,$ Topology 37 (1997), 659--664.
Mathematical Reviews (MathSciNet):
MR1604907
Digital Object Identifier: doi:10.1016/S0040-9383(97)00038-4
X. Sun, Remarks on semistability of $G$-bundles in positive characteristic, Compositio Math. 119 (1999), 41--52.
Mathematical Reviews (MathSciNet):
MR1711507
Digital Object Identifier: doi:10.1023/A:1001512029096
V. Trivedi, Semistability and Hilbert--Kunz multiplicity for curves, J. Algebra 284 (2005), 627--644.
Mathematical Reviews (MathSciNet):
MR2114572
Digital Object Identifier: doi:10.1016/j.jalgebra.2004.10.016
L. W. Tu, Semistable bundles over an elliptic curve, Adv. Math. 98 (1993), 1--26.
Mathematical Reviews (MathSciNet):
MR1212625
Digital Object Identifier: doi:10.1006/aima.1993.1011
The Michigan Mathematical Journal
