# Deligne's conjecture for automorphic motives over CM-fields, Part I: factorization

@article{Grobner2018DelignesCF, title={Deligne's conjecture for automorphic motives over CM-fields, Part I: factorization}, author={Harald Grobner and Michael Harris and Jiezhu Lin}, journal={arXiv: Number Theory}, year={2018} }

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…

## 7 Citations

Relations of rationality for special values of
Rankin–Selberg L-functions of GLn×GLm over CM-fields

- Mathematics
- 2020

In this paper we present a bridge between automorphic forms of general reductive groups and motives over number elds, hinting a translation of Deligne's conjecture for motivic L-functions into a…

Algebraicity of ratios of special values of Rankin-Selberg $L$-functions and applications to Deligne's conjecture

- Mathematics
- 2022

In this paper, we prove new cases of Blasius’ and Deligne’s conjectures on the algebraicity of critical values of tensor product L-functions and symmetric odd power L-functions associated to modular…

Square root p-adic L-functions, I : Construction
of a one-variable measure

- MathematicsTunisian Journal of Mathematics
- 2021

The Ichino-Ikeda conjecture, and its generalization to unitary groups by N. Harris, has given explicit formulas for central critical values of a large class of Rankin-Selberg tensor products.…

Special Values of L-functions for GL(n) Over a CM Field

- MathematicsInternational Mathematics Research Notices
- 2021

We prove a Galois-equivariant algebraicity result for the ratios of successive critical values of $L$-functions for ${\textrm GL}(n)/F,$ where $F$ is a totally imaginary quadratic extension of a…

Integral period relations and congruences

- MathematicsAlgebra & Number Theory
- 2022

Under relatively mild and natural conditions, we establish an integral period relations for the (real or imaginary) quadratic base change of an elliptic cusp form. This answers a conjecture of Hida…

SYNOPSIS OF THE TALK " PERIODS AND L-VALUES OF AUTOMORPHIC MOTIVES " AT SHLOSS ELMAU

- Mathematics
- 2018

A conjecture of Deligne predicts a relation between motivic L-functions and geometric periods. In this talk, we will explain an approach towards this conjecture for automorphic motives. This is a…

## References

SHOWING 1-10 OF 60 REFERENCES

Period Relations and Special Values of Rankin-Selberg L-Functions

- Mathematics
- 2017

This is a survey of recent work on values of Rankin-Selberg L-functions of pairs of cohomological automorphic representations that are critical in Deligne’s sense. The base field is assumed to be a…

COHOMOLOGICAL AUTOMORPHIC FORMS ON UNITARY GROUPS, II: PERIOD RELATIONS AND VALUES OF L-FUNCTIONS

- Mathematics
- 2007

This is the fourth in a series of articles devoted to the study of special values of L-functions of automorphic forms contributing to the cohomology of Shimura varieties attached to unitary groups,…

Beilinson–Bernstein Localization Over ℚ and Periods of Automorphic Forms

- Mathematics
- 2013

The present paper is the first in a projected series of articles whose purpose is to draw conclusions from the comparison between an arithmetic conjecture of Deligne and an analytic conjecture of…

Relations of rationality for special values of
Rankin–Selberg L-functions of GLn×GLm over CM-fields

- Mathematics
- 2020

In this paper we present a bridge between automorphic forms of general reductive groups and motives over number elds, hinting a translation of Deligne's conjecture for motivic L-functions into a…

Rationality for isobaric automorphic representations: the CM-case

- MathematicsMonatshefte fur Mathematik
- 2018

This note proves a simultaneous extension of the author’s joint result with M. Harris for critical values of Rankin–Selberg L-functions to general CM-fields F and cohomological automorphic representations.

CONDITIONAL BASE CHANGE FOR UNITARY GROUPS

- Mathematics
- 2004

Introduction. It has been known for many years that the stabilization of the Arthur-Selberg trace formula would, or perhaps we should write “will,” have important consequences for the Langlands…

Testing rationality of coherent cohomology of Shimura varieties

- Mathematics
- 2012

Let $G' \subset G$ be an inclusion of reductive groups whose real points have a non-trivial discrete series. Combining ergodic methods of Burger-Sarnak and the author with a positivity argument due…

On the stabilization of the trace formula.

- Mathematics
- 2011

This is the first volume of a projected series of two or three collections of mainly expository articles on the arithmetic theory of automorphic forms. The books are intended primarily for two groups…

Period relations for automorphic forms on unitary groups and critical values of $L$-functions

- Mathematics
- 2015

In this paper we explore some properties of periods attached to automorphic representations of unitary groups over CM fields and the critical values of their $L$-functions. We prove a formula…

Galois equivariance of critical values of $L$-functions for unitary groups

- Mathematics
- 2016

The goal of this paper is to provide a refinement of a formula proved by the first author which expresses some critical values of automorphic $L$-functions on unitary groups as Petersson norms of…