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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.
Published electronically: February 28, 2007
MathSciNet review: 2299469
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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.

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  • 1. Greg W. Anderson and Fernando Pablos Romo, Simple proofs of classical explicit reciprocity laws on curves using determinant groupoids over an Artinian local ring, Comm. Algebra 32 (2004), no. 1, 79–102. MR 2036223, 10.1081/AGB-120027853
  • 2. Asakura, M. On $ dlog$ image of $ K_2$ of elliptic surface minus singular fibers. Preprint, 2005, math. AG./0511190.
  • 3. Alexander Beilinson, Spencer Bloch, and Hélène Esnault, 𝜀-factors for Gauss-Manin determinants, Mosc. Math. J. 2 (2002), no. 3, 477–532. Dedicated to Yuri I. Manin on the occasion of his 65th birthday. MR 1988970
  • 4. Carlos Contou-Carrère, Jacobienne locale, groupe de bivecteurs de Witt universel, et symbole modéré, C. R. Acad. Sci. Paris Sér. I Math. 318 (1994), no. 8, 743–746 (French, with English and French summaries). MR 1272340
  • 5. Michiel Hazewinkel, Formal groups and applications, Pure and Applied Mathematics, vol. 78, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506881
  • 6. Kapranov, M.; Vasserot, E. Formal loops groups II: A local Riemann-Roch Theorem for determinantal gerbes. Preprint, 2005, math. AG./0509646.
  • 7. Kazuya Kato, A generalization of local class field theory by using 𝐾-groups. II, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980), no. 3, 603–683. MR 603953
  • 8. I. G. Macdonald, Symmetric functions and Hall polynomials, 2nd ed., Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1995. With contributions by A. Zelevinsky; Oxford Science Publications. MR 1354144
  • 9. Fernando Pablos Romo, A Contou-Carrère symbol on 𝐺𝑙(𝑛,𝒜((𝓉))) and a Witt residue theorem on ℳ𝒶𝓉(𝓃,Σ_{𝒞}), Int. Math. Res. Not. (2006), Art. ID 56824, 21. MR 2211145
  • 10. Fernando Pablos Romo, A generalization of the Contou-Carrère symbol, Israel J. Math. 141 (2004), 39–60. MR 2063024, 10.1007/BF02772210
  • 11. John Tate, Residues of differentials on curves, Ann. Sci. École Norm. Sup. (4) 1 (1968), 149–159. MR 0227171
  • 12. Witt, E. Zyklische Körper und Algebren der Charakteristik $ p$ vom Grad $ p^n$. J. Reine Angew. Math. 1937, 176, 126-140.

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Additional Information

Fernando Pablos Romo
Affiliation: Departamento de Matemáticas, Universidad de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca, España

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.