I want to know if there exists a set of motives that corresponds to automorphic representations of a reductive group. Such a set must be divided into sets of the same L(or ε）function and satisfy the strong multiplicity one theorem. Do we know such a set and packets exist without any artificial flavor (conjecturally)?
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Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Aug 28 '21 at 13:30
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Do we have a (conjectural) classification of motives in terms of L(or ε)-functions that matches the packet theory of automorphic representations of a reductive group? How is GL2-case(i.e. an equivalent form of modularity conjecture) generalize to a reductive group? – Takahiro Matsuda Aug 28 '21 at 14:18