Another algebraic proof of Weil's reciprocity

Emma Previato

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1991)

  • Volume: 2, Issue: 2, page 167-171
  • ISSN: 1120-6330

Abstract

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The Burchnall-Chaundy-Krichever correspondence which converts meromorphic functions on a curve into differential operators is used to interpret Weil's reciprocity as the calculation of a resultant.

How to cite

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Previato, Emma. "Another algebraic proof of Weil's reciprocity." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 2.2 (1991): 167-171. <http://eudml.org/doc/244084>.

@article{Previato1991,
abstract = {The Burchnall-Chaundy-Krichever correspondence which converts meromorphic functions on a curve into differential operators is used to interpret Weil's reciprocity as the calculation of a resultant.},
author = {Previato, Emma},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Riemann surface; Ordinary differential operator; Resultant; resultants; differential operators},
language = {eng},
month = {6},
number = {2},
pages = {167-171},
publisher = {Accademia Nazionale dei Lincei},
title = {Another algebraic proof of Weil's reciprocity},
url = {http://eudml.org/doc/244084},
volume = {2},
year = {1991},
}

TY - JOUR
AU - Previato, Emma
TI - Another algebraic proof of Weil's reciprocity
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1991/6//
PB - Accademia Nazionale dei Lincei
VL - 2
IS - 2
SP - 167
EP - 171
AB - The Burchnall-Chaundy-Krichever correspondence which converts meromorphic functions on a curve into differential operators is used to interpret Weil's reciprocity as the calculation of a resultant.
LA - eng
KW - Riemann surface; Ordinary differential operator; Resultant; resultants; differential operators
UR - http://eudml.org/doc/244084
ER -

References

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  1. ARBARELLO, E. - DE CONCINI, C. - KAC, V. G., The infinite wedge representation and the reciprocity law for algebraic curves. Preprint 1988. Zbl0699.22028MR1141196
  2. FLASCHKA, H., Towards an algebro-geometric interpretation of the Neumann system. Tôhoku Math. J., 36, 1984, 407-426. Zbl0582.35102MR756025DOI10.2748/tmj/1178228807
  3. FLOQUET, G., Sur la théorie des équations différentielles linéaires. Ann. Sci. de l'Ecole Norm. Super., 8, 1879, 3-132. MR1508684JFM11.0239.01
  4. GRIFFITHS, P. A. - HARRIS, J., Principles of Algebraic Geometry. John Wiley and Sons, New York1978. Zbl0836.14001MR1288523
  5. LANG, S., Algebra. Addison-Wesley, Reading Mass.1965. Zbl0848.13001MR197234
  6. MUMFORD, D., An algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg-de Vries equation and related nonlinear equations. Proceedings of Intern. Symposium on Algebraic Geometry (Kyoto), Kino Kuniya Book Store, 1978, 115-153. Zbl0423.14007MR578857
  7. PREVIATO, E., Generalized Weierstrass P functions and K ⁢ P flows in affine space. Comment. Math. Helv., 62, 1987, 292-310. Zbl0638.14024MR896099DOI10.1007/BF02564449
  8. PREVIATO, E., The Calogero-Moser-Krichever system and elliptic Boussinesq solitons. In: J. HARNADJ. E. MARSDEN (eds.), Proceedings CRM Workshop, CRM Press, Montréal1990, 57-67. Zbl0749.35047MR1110372
  9. WEIL, A., Sur les fonctions algébriques à corps de constantes fini. C.R. Acad. Sci. Paris, 210, 1940, 592-594. MR2863JFM66.0135.01

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