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Galois Representations - math.ias.edu

Galois Representations R. Taylor . Abstract In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking Representations of Galois groups with algebraic geometry, complex analysis and discrete sub- groups of Lie groups. In the second part we briefly review some limited recent progress on these conjectures. 2000 Mathematics Subject Classification: 11F80. Keywords and Phrases: Galois Representations , L-function, automorphic forms. Introduction This is a longer version of my talk at the Beijing ICM. The version to be published in the proceedings of the ICM was edited in an attempt to make it meet restrictions on length suggested by the publishers.

The Galois theory of Q is most interesting when one looks not only at GQ as an abstract (topological) group, but as a group with certain additional structures associated to the prime numbers.

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