
arXiv: math/0212403
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 subgroups of Lie groups. In the second part we briefly review some limited recent progress on these conjectures.
11F80, Representation-theoretic methods; automorphic representations over local and global fields, Mathematics - Number Theory, Galois representations, \(L\)-functions, Research exposition (monographs, survey articles) pertaining to number theory, FOS: Mathematics, Number Theory (math.NT), modularity, Langlands-Weil conjectures, nonabelian class field theory
11F80, Representation-theoretic methods; automorphic representations over local and global fields, Mathematics - Number Theory, Galois representations, \(L\)-functions, Research exposition (monographs, survey articles) pertaining to number theory, FOS: Mathematics, Number Theory (math.NT), modularity, Langlands-Weil conjectures, nonabelian class field theory
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