Reciprocity in the Langlands Program
by Frank Calegari
Abstract: How much does the cohomology of an algebraic variety tell us about the variety itself? The answer, at least according to a conjecture of Tate, is quite a lot. In this talk, I will try to outline the relationship --- mostly conjectural --- between algebraic varieties, their cohomology, and a special class of functions (L-functions) generalizing the Riemann zeta function.
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