Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications

Jan Hendrik Bruinier, Benjamin Howard, Stephen S. Kudla, Michael Rapoport, Tonghai Yang

Type: Article

Publication Date: 2020-01-01

Citations: 10

DOI: https://doi.org/10.24033/ast.1127

Abstract

We prove two formulas in the style of the Gross-Zagier theorem, relating derivatives of L-functions to arithmetic intersection pairings on a unitary Shimura variety. We also prove a special case of Colmez's conjecture on the Faltings heights of abelian varieties with complex multiplication. These results are derived from the authors' earlier results on the modularity of generating series of divisors on unitary Shimura varieties.

Locations

arXiv (Cornell University) - View - PDF
Astérisque - View

Similar Works

Action	Title	Year	Authors
+	Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications	2017	Jan Hendrik Bruinier Benjamin Howard Stephen S. Kudla Michael Rapoport Tonghai Yang
+	Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu)	2022	Congling Qiu
+ PDF Chat	Modularity of generating series of divisors on unitary Shimura varieties	2020	Jan Hendrik Bruinier Benjamin Howard Stephen S. Kudla Michael Rapoport Tonghai Yang
+	Modularity of generating series of divisors on unitary Shimura varieties	2017	Jan Hendrik Bruinier Benjamin Howard Stephen S. Kudla Michael Rapoport Tonghai Yang
+ PDF Chat	Pullback of arithmetic theta series and its modularity for unitary Shimura curves	2024	Qiao He Yousheng Shi Tonghai Yang
+ PDF Chat	Faltings heights of CM cycles and derivatives of L-functions	2009	Jan Hendrik Bruinier Tonghai Yang
+ PDF Chat	Arithmetic of Borcherds products	2020	Benjamin Howard Keerthi Madapusi Pera
+	Arithmetic of Borcherds products	2017	Benjamin Howard Keerthi Madapusi Pera
+	Faltings heights of CM cycles and derivatives of L-functions	2008	Jan Hendrik Bruinier Tonghai Yang
+ PDF Chat	Faltings heights of abelian varieties with complex multiplication	2018	Fabrizio Andreatta Eyal Z. Goren Benjamin Howard Keerthi Madapusi Pera
+ PDF Chat	Height pairings on orthogonal Shimura varieties	2017	Fabrizio Andreatta Eyal Z. Goren Benjamin Howard Keerthi Madapusi Pera
+	Heights of CM cycles and derivatives of L-series	2017	Yara Elias Tian An Wong
+	Intersection formulas on moduli spaces of unitary shtukas	2023	Yongyi Chen Benjamin Howard
+ PDF Chat	Heights of Kudla–Rapoport divisors and derivatives of $$L$$ L -functions	2014	Jan Hendrik Bruinier Benjamin Howard Tonghai Yang
+	Faltings heights of abelian varieties with complex multiplication	2015	Fabrizio Andreatta Eyal Z. Goren Benjamin Howard Keerthi Madapusi Pera
+	Faltings heights of abelian varieties with complex multiplication	2015	Fabrizio Andreatta Eyal Z. Goren Benjamin Howard Keerthi Madapusi Pera
+	Modular Heights of Quaternionic Shimura Curves	2022	Xinyi Yuan
+ PDF Chat	On two arithmetic theta lifts	2018	Stephan Ehlen Siddarth Sankaran
+	Modular Forms and Special Cycles on Shimura Curves. (AM-161)	2006	Stephen S. Kudla Michael Rapoport Tonghai Yang
+	Generating series of intersection volumes of special cycles on unitary Shimura varieties	2017	Zavosh Amir-Khosravi

Works That Cite This (10)

Action	Title	Year	Authors
+	Linear invariance of intersections on unitary Rapoport-Zink spaces	2018	Benjamin Howard
+	CM fields of Dihedral type and the Colmez conjecture	2017	Tonghai Yang Hongbo Yin
+ PDF Chat	Modularity of generating series of divisors on unitary Shimura varieties	2020	Jan Hendrik Bruinier Benjamin Howard Stephen S. Kudla Michael Rapoport Tonghai Yang
+	Arithmetic volumes of unitary Shimura varieties	2021	Jan Hendrik Bruinier Benjamin Howard
+ PDF Chat	Signature (n − 2,2) CM types and the unitary Colmez conjecture	2018	Solly Parenti
+ PDF Chat	Some cases of Kudla’s modularity conjecture for unitary Shimura varieties	2022	Jiacheng Xia
+	CM fields of Dyhedral type and the Colmez conjecture	2017	Tonghai Yang Hongbo Yin
+	Remarks on generating series for special cycles	2019	Stephen S. Kudla
+	Difference of modular functions and their CM value factorization	2017	Tonghai Yang Hongbo Yin
+	The construction of Green currents and singular theta lifts for unitary groups	2019	Jens Funke Eric Hofmann

Works Cited by This (19)

Action	Title	Year	Authors
+ PDF Chat	Special Cycles and Derivatives of Eisenstein Series	2004	Stephen S. Kudla
+	On the periods of abelian integrals and a formula of Chowla and Selberg	1978	Benedict H. Gross
+ PDF Chat	COHOMOLOGICAL ARITHMETIC CHOW RINGS	2006	José Ignacio Burgos Gil J. Kramer Ulf Kühn
+ PDF Chat	On the Fourier coefficients of automorphic forms at various cusps and some applications to Rankin's convolution	1976	Tetsuya Asai
+ PDF Chat	Borcherds products and arithmetic intersection theory on Hilbert modular surfaces	2007	Jan Hendrik Bruinier José Ignacio Burgos Gil Ulf Kühn
+	Special Values of Green Functions at Big CM Points	2011	Jan Hendrik Bruinier Stephen S. Kudla Tai Yang
+ PDF Chat	On Colmez’s product formula for periods of CM-abelian varieties	2012	Andrew Obus
+ PDF Chat	Arithmetic intersection theory	1990	Henri Gillet Christophe Soulé
+ PDF Chat	Complex multiplication cycles and Kudla-Rapoport divisors, II	2015	Benjamin Howard
+	Periodes des Varietes Abeliennes a Multiplication Complexe	1993	Pierre Colmez