Factorization of p-adic Rankin L-series

• 成果类型: Article
• 署名作者: Dasgupta, Samit
• 署名单位: University of California System; University of California Santa Cruz
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0634-4
• 发表日期: 2016
• 页码: 221-268
• 关键词: finiteness theorem; euler systems; conjecture; square; cycles

摘要

We prove that the p-adic L-series of the tensor square of a p-ordinary modular form factors as the product of the symmetric square p-adic L-series of the form and a Kubota-Leopoldt p-adic L-series. This establishes a generalization of a conjecture of Citro. Greenberg's exceptional zero conjecture for the adjoint follows as a corollary of our theorem. Our method of proof follows that of Gross, who proved a factorization result for the Katz p-adic L-series associated to the restriction of a Dirichlet character. Whereas Gross's method is based on comparing circular units with elliptic units, our method is based on comparing these same circular units with a new family of units (called Beilinson-Flach units) that we construct. The Beilinson-Flach units are constructed using Bloch's intersection theory of higher Chow groups applied to products of modular curves. We relate these units to special values of classical and p-adic L-functions using work of Beilinson (as generalized by Lei-Loeffler-Zerbes) in the archimedean case and Bertolini-Darmon-Rotger (as generalized by Kings-Loeffler-Zerbes) in the p-adic case. Central to our method are two compatibility theorems regarding Bloch's intersection pairing and the classical and p-adic Beilinson regulators defined on higher Chow groups.