Hasse-Witt matrices and Kummer extension

Francis J. Sullivan

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1988)

  • Volume: 82, Issue: 3, page 405-411
  • ISSN: 1120-6330

Abstract

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A simple calculation of the Hasse-Witt matrix is used to give examples of curves which are Kummer coverings of the projective line and which have easily determined p-rank. A family of curve carrying non-classical vector bundles of rank 2 is also given.

How to cite

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Sullivan, Francis J.. "Hasse-Witt matrices and Kummer extension." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 82.3 (1988): 405-411. <http://eudml.org/doc/287422>.

@article{Sullivan1988,
abstract = {A simple calculation of the Hasse-Witt matrix is used to give examples of curves which are Kummer coverings of the projective line and which have easily determined p-rank. A family of curve carrying non-classical vector bundles of rank 2 is also given.},
author = {Sullivan, Francis J.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Jacobian variety; Hasse-Witt matrix; Cartier operator; characteristic ; Kummer extensions; Kummer coverings; -rank; curves carrying non-classical vector bundles},
language = {eng},
month = {9},
number = {3},
pages = {405-411},
publisher = {Accademia Nazionale dei Lincei},
title = {Hasse-Witt matrices and Kummer extension},
url = {http://eudml.org/doc/287422},
volume = {82},
year = {1988},
}

TY - JOUR
AU - Sullivan, Francis J.
TI - Hasse-Witt matrices and Kummer extension
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1988/9//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 3
SP - 405
EP - 411
AB - A simple calculation of the Hasse-Witt matrix is used to give examples of curves which are Kummer coverings of the projective line and which have easily determined p-rank. A family of curve carrying non-classical vector bundles of rank 2 is also given.
LA - eng
KW - Jacobian variety; Hasse-Witt matrix; Cartier operator; characteristic ; Kummer extensions; Kummer coverings; -rank; curves carrying non-classical vector bundles
UR - http://eudml.org/doc/287422
ER -

References

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  3. GRIFFITHS, P. and HARRIS, I. - Principles of Algebraic Geometry, New York, J. Wiley & Sons (1978). Zbl0836.14001MR507725
  4. GUNNING, R. - Lectures on Riemann Surfaces, PrincetonU. Press, 1967. Zbl0387.32008MR207977
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  6. HASSE, H. and WITT, E. - Zyklische unverzweigte Erweiterungskörper von Primazahlgrade überein algebraischen Funktionenkörper, der Charakteristik p, «Monathft. Math. Phy.», 43, 477-493 (1936). Zbl0013.34102JFM62.0112.01
  7. IGUSA, J. - On the Transformation Theory of Elliptic Functions, «Amer. J. Math.», 81, 436-452 (1959). Zbl0131.28102MR104668
  8. MADDEN, D. - Arithmetic in Generalized Artin-Schreier Extensions of k ⁢ ( x ) , «Journ. of Number Theory», 10, 303-323 (1978). Zbl0384.12008MR506641DOI10.1016/0022-314X(78)90027-6
  9. MILLER, L. - Curves with Invertible Hasse-Witt Matrix, «Math. Ann.», 197, 123-125 (1977). Zbl0235.14009MR314849
  10. SERRE, J.P. - Sur la topologie des variétés algébriques en characteristique p, «Sympos. Internac. Topol. Alg. Mexico City», 24-53 (1956). Zbl0098.13103MR98097
  11. SUBRAO, D. - Thep-rank of Artin-Schreir Curves, «Manuscripta Math.», 16, 169-193 (1975). Zbl0321.14017MR376693
  12. WEIERSTRASS, K. - Gesammelte Werke, IV, 135-145 (1905). 
  13. YUI, N. - On the Jacobian Variety of the Fermat Curve, «Journ. of Algebra», 65, 1-34 (1980). Zbl0437.14015MR578793DOI10.1016/0021-8693(80)90236-7

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