Is there a Galois correspondence in motivic Galois theory ? If so, is there a mathematical work on this correspondence that i can find on the net ?
Thanks in advance for your help.
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$\begingroup$ In any Tannakian category, including the conjectural Tannakian category of motives, there is a Galois correspondence between subcategories stable under subobjects, quotients, duals, sums, and tensor products (I might be missing a condition there) and normal subgroups. I don't know how much more there is to say there so I don't know if anyone has studied this. $\endgroup$– Will SawinCommented Mar 4, 2021 at 19:12
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$\begingroup$ @Will: should the notion of L-rig introduced in mathoverflow.net/questions/372349/… be categorized, would it give rise to a Tannakian category and that way "explain" why L-functions of arithmetic interest ought to be motivic? I can ask a separate question if needed. $\endgroup$– Sylvain JULIENCommented Mar 4, 2021 at 19:49
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$\begingroup$ I know very little about this matters; yet my impression that needs some Langlands-type conjectures to make reasonable(??) L-functions motivic. And several people studied the motivic Galois group. This is a rather complicated thing. and Joseph Ayoub is a specialist. $\endgroup$– Mikhail BondarkoCommented Mar 5, 2021 at 10:42
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