Generalized reciprocity laws

Muñoz Porras, José; Romo, Fernando

doi:10.1090/S0002-9947-08-04554-6

Generalized reciprocity laws
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by José M. Muñoz Porras and Fernando Pablos Romo PDF

Trans. Amer. Math. Soc. 360 (2008), 3473-3492 Request permission

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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