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• W2787003206 abstract "This is the first of two papers devoted to the relations between Deligne's conjecture on critical values of motivic $L$-functions and the multiplicative relations between periods of arithmetically normalized automorphic forms on unitary groups. The present paper combines the Ichino-Ikeda-Neal Harris (IINH) formula with an analysis of cup products of coherent cohomological automorphic forms on Shimura varieties to establish relations between certain automorphic periods and critical values of Rankin-Selberg and Asai $L$-functions of $GL(n)times GL(m)$ over CM fields. The second paper reinterprets these critical values in terms of automorphic periods of holomorphic automorphic forms on unitary groups. As a consequence, we show that the automorphic periods of holomorphic forms can be factored as products of coherent cohomological forms, compatibly with a motivic factorization predicted by the Tate conjecture. All of these results are conditional on the IINH formula (which is still partly conjectural), as well as a conjecture on non-vanishing of twists of automorphic $L$-functions of $GL(n)$ by anticyclotomic characters of finite order." @default.
• W2787003206 created "2018-02-23" @default.
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• W2787003206 date "2018-02-08" @default.
• W2787003206 modified "2023-09-27" @default.
• W2787003206 title "Deligne's conjecture for automorphic motives over CM-fields, Part I: factorization" @default.
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