Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A new explicit expression of the Contou-Carrère symbol


Author: Fernando Pablos Romo
Journal: Proc. Amer. Math. Soc. 135 (2007), 1977-1985
MSC (2000): Primary 19F15, 19C20.
DOI: https://doi.org/10.1090/S0002-9939-07-08690-X
Published electronically: February 28, 2007
MathSciNet review: 2299469
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The aim of this note is to offer a new explicit expression of the Contou-Carrère symbol that depends only on a product of a finite number of terms. As an application, we obtain an explicit formula for a Witt Residue.


References [Enhancements On Off] (What's this?)

  • 1. Anderson, G. W.; Pablos Romo, F. Simple Proofs of Classical Explicit Reciprocity Laws on Curves using Determinant Grupoids over an Artinian Local Ring. Comm. Algebra. 2004, 32(1), 79-102. MR 2036223 (2005d:11099)
  • 2. Asakura, M. On $ dlog$ image of $ K_2$ of elliptic surface minus singular fibers. Preprint, 2005, math. AG./0511190.
  • 3. Beilinson, A.; Bloch S.; Esnault H. $ \epsilon$-factors for Gauss-Manin determinants. Moscow Math. J. 2002, 2(3), 477-532.MR 1988970 (2004m:14011)
  • 4. Contou-Carrere, C. Jacobienne Locale, Groupe de Bivecteurs de Witt Universel et Symbole Modéré. C.R. Acad. Sci. Paris. 1994, 318, Série I, 743-746.MR 1272340 (95c:14059)
  • 5. Hazewinkel, M., Formal Groups and Applications, Academic Press, New York, San Francisco, London, 1978. MR 0506881 (82a:14020)
  • 6. Kapranov, M.; Vasserot, E. Formal loops groups II: A local Riemann-Roch Theorem for determinantal gerbes. Preprint, 2005, math. AG./0509646.
  • 7. Kato, K. A Generalization of local class field theory by using $ K$-groups II. J. Fac. Sci. Univ. Tokyo Sect. IA 1980, 27(3), 603-683.MR 0603953 (83g:12020a)
  • 8. Macdonald, I. G., Symmetric Functions and Hall Polynomials, Oxford Science Publications, second edition, Oxford, 1995. MR 1354144 (96h:05207)
  • 9. Pablos Romo, F. A Contou-Carrère symbol on $ \gl(n,A((t)))$ and a Witt Residue Theorem on $ \mat (n,\Sigma_C)$. Int. Math. Res. Not. 2006, Article ID 56824, 1-21. MR 2211145 (2006m:11092)
  • 10. Pablos Romo, F. A Generalization of the Contou-Carrère symbol. Israel J. Math. 2004, 141, 39-60. MR 2063024 (2005g:11115)
  • 11. Tate, J. Residues of Differentials on Curves. Ann. Scient. Éc. Norm. Sup. 1968, 4a série, 1, 149-159.MR 0227171 (37:2756)
  • 12. Witt, E. Zyklische Körper und Algebren der Charakteristik $ p$ vom Grad $ p^n$. J. Reine Angew. Math. 1937, 176, 126-140.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 19F15, 19C20.

Retrieve articles in all journals with MSC (2000): 19F15, 19C20.


Additional Information

Fernando Pablos Romo
Affiliation: Departamento de Matemáticas, Universidad de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca, España
Email: fpablos@usal.es

DOI: https://doi.org/10.1090/S0002-9939-07-08690-X
Keywords: Contou-Carr\`{e}re symbol, explicit expression, artinian local ring, Witt Residue
Received by editor(s): February 6, 2006
Received by editor(s) in revised form: February 23, 2006, and March 1, 2006
Published electronically: February 28, 2007
Additional Notes: This work was partially supported by the DGESYC research contract no. BFM2003-00078 and Castilla y León regional government contract SA071/04.
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society