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Deligne's conjecture for automorphic motives over CM-fields, Part I: factorization | | Harald Grobner
; Michael Harris
; Jie Lin
; | | Date: |
8 Feb 2018 | | 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
$GL(n) imes GL(m)$ 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. | | Source: | arXiv, 1802.2958 | | Services: | Forum | Review | PDF | Favorites | |
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