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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Generalized reciprocity laws


Authors: José M. Muñoz Porras and Fernando Pablos Romo
Journal: Trans. Amer. Math. Soc. 360 (2008), 3473-3492
MSC (2000): Primary 14H05, 19F15, 14M15
Published electronically: February 27, 2008
MathSciNet review: 2386233
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Abstract: The aim of this paper is to give an abstract formulation of the classical reciprocity laws for function fields that could be generalized to the case of arbitrary (non-commutative) reductive groups as a first step to finding explicit non-commutative reciprocity laws. The main tool in this paper is the theory of determinant bundles over adelic Sato Grassmannians and the existence of a Krichever map for rank $ n$ vector bundles.


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Additional Information

José M. Muñoz Porras
Affiliation: Departamento de Matemáticas, Universidad de Salamanca, Plaza de la Merced 1-4, Salamanca 37008, Spain
Email: jmp@usal.es

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

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04554-6
PII: S 0002-9947(08)04554-6
Received by editor(s): March 8, 2006
Published electronically: February 27, 2008
Additional Notes: This work was partially supported by DGI research contract no. MTM2006-07618 and Castilla y León regional government contract SA071/04.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.