79
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

An Algebraic-Geometric Method for Constructing Generalized Local Symbols on Curves

Pages 2142-2163 | Received 20 Nov 2008, Published online: 14 Jun 2010

REFERENCES

  • Arbarello , E. , de Concini , C. , Kac , V. G. ( 1989 ). The infinite wedge representation and the reciprocity law for algebraic curves . In: Proc. of Symposia in Pure Mathematics . American Mathematical Society, Vol. 49. Part I , pp. 171 – 190 .
  • Anderson , G. W. , Pablos Romo , F. ( 2004 ). Simple proofs of classical explicit reciprocity laws on curves using determinant grupoids over an artinian local ring . Comm. Algebra 32 ( 1 ): 79 – 102 .
  • Beilinson , A. , Bloch , S. , Esnault , H. ( 2002 ). ε-Factors for Gauss-Manin determinants . Moscow Math. J. 2 ( 3 ): 477 – 532 .
  • Bell , R. A. (1996). On properties of the n-dimensional norm residue symbol in higher local class field theory. J. Pure Appl. Algebra 108(1):1–6.
  • Contou-Carrère , C. ( 1994 ). Jacobienne Locale, Groupe de Bivecteurs de Witt Universel et Symbole Modéré . C. R. Acad. Sci. Paris, t. 318 ( Série I ): 743 – 746 .
  • Deligne , P. ( 1991 ). Le Symbole Modéré . I. H. E. S., Publications Mathematiques 73 : 147 – 181 .
  • Grothendieck , A. , Dieudonné , J. A. ( 1971 ). Eléments de Géométrie Algébrique . Berlin-Heidelberg-New York : Springer-Verlag .
  • Grothendieck , A. ( 1972 ). Foncteurs Fibres, Supports, Etude Cohomologique des Morfismes Fines, SGA 4, Tome 2, Berlin-Heidelberg-New York: Springer-Verlag, pp. 367–412 .
  • Grothendieck , A. (1961/62). TDTE VI: Les Schémas de Picard: Propiétés Générales, F.G.A., Seminaire Bourbaki, t. 14.
  • Hazewinkel , M. ( 1978 ). Formal Groups and Applications . New York-San Francisco-London : Academic Press .
  • Howe , Everett W. ( 1996 ). The Weil pairing and the Hilbert symbol . Math. Ann. 305 ( 2 ): 387 – 392 .
  • Milnor , J. ( 1971 ). Introduction to Algebraic K-Theory . Annals of Mathematics Studies, Princeton University Press .
  • Mumford , D. , Nori , M. , Norman , P. ( 1991 ). Tata Lectures on Theta III . Boston-Basel-Berlin : Birkhäuser .
  • Mumford , D. ( 1970 ). Abelian Varieties . Bombay : Oxford University Press .
  • Pablos Romo , F. ( 2004 ). A generalization of the Contou-Carrère symbol . Israel J. Math. 141 : 39 – 60 .
  • Pablos Romo , F. ( 2003 ). A note on Steinberg symbols on algebraic curves . Comm. Algebra 31 ( 2 ): 981 – 990 .
  • Pablos Romo , F. ( 1994 ). Construcción Canónica de Cúspides y Aproximación a su Jacobiana . Extracta Math. 9 ( 1 ): 21 – 27 .
  • Pablos Romo , F. ( 2002 ). On the Tame symbol of an algebraic curve . Comm. Algebra 30 ( 9 ): 4349 – 4368 .
  • Pablos Romo , F. ( 2004 ). Theta groups over extensions of abelian varieties by unipotent groups . Moscow Math. J. 4 ( 2 ): 501 – 508 .
  • Rosenlicht , M. ( 1954 ). Generalized Jacobian varieties . Ann. of Math. 59 : 505 – 530 .
  • Rosenlicht , M. ( 1957 ). A universal mapping property of generalized Jacobian varieties . Ann. of Math. 66 : 80 – 88 .
  • Schmidt , H. L. ( 1936 ). Über das Reziprozitätsgesatz in relativ-zyklischen algebraischen Funktionkörpern mit endlichem Konstantenkörper . Math. Z. 40 : 94 – 109 .
  • Serre , J. P. ( 1959 ). Groupes Algébriques et Corps de Classes . Paris : Hermann .
  • Communicated by C. Pedrini.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.