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On the Behavior of Extensions of Vector Bundles Under the Frobenius Map

Published online by Cambridge University Press:  22 January 2016

Hiroshi Tango*
Affiliation:
Department of Mathematics, Kyoto University
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Let k be an algebraically closed field of characteristic p > 0, and let X be a curve defined over k. The aim of this paper is to study the behavior of the Frobenius map F*: H1(X, E)H1(X, F*E) for a vector bundle E.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

[1] Atiyah, M. F., Vector bundle over an elliptic curve. Proc. Lond. Math. Soc. (3) 7 (1957) 414452.Google Scholar
[2] Gieseker, D., p-ample bundles and their Chern classes. Nagoya Math. J. 43 (1971).Google Scholar
[3] Grothendieck, A. and Dieudonné, J., Elément de géométrie algébrique. Publ. Math. I. H. E. S. Google Scholar
[4] Hartshorne, R., Ample vector bundles. Publ. Math. I. H. E. S. 29 (1966).Google Scholar
[5] Hartshorne, R., Ample vector bundles on curves. Nagoya Math. J. 43 (1971).Google Scholar
[6] Maruyama, M., On classification of ruled surfaces. Kinokuniya book store Co. Ltd. Lectures in mathematics Dep. of Math. Kyoto Univ. 3.Google Scholar
[7] Nagata, M., On self intersection number of a section on a ruled surface. Nagoya Math. J. 37 (1970).Google Scholar
[8] Oda, T., Vector bundle on an elliptic curve. Nagoya Math. J. 43 (1971).Google Scholar
[9] Serre, J. P., Sur la topologie des variété algébraiques en characteristic p. Sympos. Internac. Topologia algebraica. Mexico City. (1956). 2453. Univ. Nac. Aut. Mexico. 1958. MR 20. 4559.Google Scholar
[10] Cartier, P., Questions de rationalité des diviseurs en géométrie algébrique. Bull. Soc. Math. France. 86 (1958).Google Scholar
[11] Seshadri, C. S., L’opération de Cartier. Applications. Séminair Chevalley 3 (1958–59) Variétés de Picard.Google Scholar