ALGEBRAIC MONODROMY GROUPS OF G-VALUED l-ADIC REPRESENTATIONS OF Gal(Q/Q)
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چکیده
A connected reductive algebraic group G is said to be an l-adic algebraic monodromy group for ΓQ if there is a continuous homomorphism Gal(Q/Q)→ G(Ql) with Zariski-dense image. In this paper, we give a classification of connected l-adic algebraic monodromy groups for Gal(Q/Q), in particular producing the first such examples for SLn,Sp2n,Spinn and E sc 6 . To do this, we start with a mod-l representation of Gal(Q/Q) coming from the Weyl group of G and use a variation of Stefan Patrikis’ generalization of a method of Ravi Ramakrishna to produce its desired l-adic lifts.
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تاریخ انتشار 2017