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Reciprocity Law for Compatible Systems of Abelian mod $p$ Galois Representations

Published online by Cambridge University Press:  20 November 2018

Chandrashekhar Khare
Chandrashekhar Khare*
Affiliation:
Department of Mathematics, University of Utah, 155 S 1400 E, Salt Lake City, UT 84112, U.S.A., e-mail: shekhar@math.utah.edu
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Abstract

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The main result of the paper is a reciprocity law which proves that compatible systems of semisimple, abelian mod $p$ representations (of arbitrary dimension) of absolute Galois groups of number fields, arise from Hecke characters. In the last section analogs for Galois groups of function fields of these results are explored, and a question is raised whose answer seems to require developments in transcendence theory in characteristic $p$.

Keywords

11F80
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 6 , 01 December 2005 , pp. 1215 - 1223
Copyright
Copyright © Canadian Mathematical Society 2005

References

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