Global geometrised Rankin-Selberg method for GL(n)

Local geometrised Rankin-Selberg method for GL(n)

Following Laumon [10], to a nonramified $\ell$-adic local system $E$ of rank $n$ on a curve $X$ one associates a complex of $\ell$-adic sheaves $_n{\cal K}_E$ on the moduli stack of rank $n$ vector bundles on $X$ with a section, which is cuspidal and satisfies Hecke property for $E$. This is a geometric counterpart of the well-known construction due to Shalika [17] and Piatetski-Shapiro [16]. We express the cohomology of the tensor product $_n{\cal K}_{E_1}\otimes {_n{\cal K}_{E_2}}$ in terms of cohomology of the symmetric powers of $X$. This may be considered as a geometric interpretation of …

模形式Rankin-Selberg积的正则子

Regulators for Rankin-Selberg products of modular forms

该论文证明了两个模形式Rankin-Selberg积的L-函数非临界值上Beilinson猜想的一个弱版本。

On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives

In this article, we study the Beilinson-Bloch-Kato conjecture for motives corresponding to the Rankin-Selberg product of conjugate self-dual automorphic representations, within the framework of the Gan-Gross-Prasad conjecture. We show that if the central critical value of the Rankin-Selberg $L$-function does not vanish, then the Bloch-Kato Selmer group with coefficients in a favorable field of the corresponding motive vanishes. We also show that if the class in the Bloch-Kato Selmer group constructed from certain diagonal cycle does not vanish, which is conjecturally equivalent to the nonvanis…

关于Rankin–Selberg动机的Selmer群的有界性综述

Survey on bounding Selmer groups for Rankin--Selberg motives

本文综述作者此前关于Rankin–Selberg动机的Beilinson–Bloch–Kato猜想研究，并结合X. Zhu的范畴局部Langlands纲领提出新观察与推测。

Eisenstein Cohomology and ratios of critical values of Rankin-Selberg L-functions

This is an announcement of results on rank-one Eisenstein cohomology of GL(N), with N > 1 an odd integer, and algebraicity theorems for ratios of successive critical values of certain Rankin-Selberg L-functions for GL(n) x GL(n') when n is even and n' is odd.

Rankin-Selberg L-函数的导数与广义Heegner圈的高度

Derivatives of Rankin-Selberg $L$-functions and heights of generalized Heegner cycles

本文证明权2k新形式与无穷型(2t,0)非分歧虚二次Hecke特征的Rankin-Selberg L-函数中心导数等于广义Heegner圈的Beilinson-Bloch高度，统一推广了Gross-Zagier公式和Zhang的高权公式。