Galois representations with conjectural connections to arithmetic cohomology
نویسندگان
چکیده
منابع مشابه
Three-dimensional Galois Representations with Conjectural Connections to Arithmetic Cohomology
In [4], Ash and Sinnott conjecture that any Galois representation having niveau 1 which satisfies a certain parity condition is attached in a specific way to a Hecke eigenclass in cohomology, and they make a prediction about exactly where the relevant cohomology class should lie. They give examples of reducible three-dimensional representations which appear to be attached to cohomology eigencla...
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In this paper we extend a conjecture of Ash and Sinnott relating niveau one Galois representations to the mod p cohomology of congruence subgroups of SLn(Z) to include Galois representations of higher niveau. We then present computational evidence for our conjecture in the case n = 3 in the form of three-dimensional Galois representations which appear to correspond to cohomology eigenclasses as...
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In this essay we briefly introduce the main ideas behind the theory of studying algebraic varieties over a number field by constructing associated Galois representations, and see how this can be understood naturally in the context of an extension of monodromy theory from geometry. We then, following Deligne’s original method, use some of these ideas to prove the Riemann Hypothesis for varieties...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2002
ISSN: 0012-7094
DOI: 10.1215/s0012-9074-02-11235-6