Picard Modular Surfaces

Automorphic vector bundles with global sections on -schemes

Compositio Mathematica ◽

10.1112/s0010437x18007467 ◽

2018 ◽

Vol 154 (12) ◽

pp. 2586-2605 ◽

Cited By ~ 4

Author(s):

Wushi Goldring ◽

Jean-Stefan Koskivirta

Keyword(s):

Vector Bundles ◽

Shimura Varieties ◽

Surjective Morphism ◽

General Conjecture ◽

Picard Modular Surfaces

A general conjecture is stated on the cone of automorphic vector bundles admitting nonzero global sections on schemes endowed with a smooth, surjective morphism to a stack of $G$-zips of connected Hodge type; such schemes should include all Hodge-type Shimura varieties with hyperspecial level. We prove our conjecture for groups of type $A_{1}^{n}$, $C_{2}$, and $\mathbf{F}_{p}$-split groups of type $A_{2}$ (this includes all Hilbert–Blumenthal varieties and should also apply to Siegel modular $3$-folds and Picard modular surfaces). An example is given to show that our conjecture can fail for zip data not of connected Hodge type.

Download Full-text

On l-adic representations attached to Hilbert and Picard modular surfaces

Journal of Number Theory ◽

10.1016/j.jnt.2009.10.006 ◽

2010 ◽

Vol 130 (5) ◽

pp. 1197-1211

Author(s):

Cristian Virdol

Keyword(s):

Picard Modular Surfaces

Download Full-text

Integral cohomology of certain Picard modular surfaces

Journal of Number Theory ◽

10.1016/j.jnt.2013.07.015 ◽

2014 ◽

Vol 134 ◽

pp. 13-28

Author(s):

Dan Yasaki

Keyword(s):

Integral Cohomology ◽

Picard Modular Surfaces

Download Full-text

Degeneration of Hodge structures over Picard modular surfaces

International Journal of Number Theory ◽

10.1142/s1793042117500622 ◽

2017 ◽

Vol 13 (05) ◽

pp. 1145-1164 ◽

Cited By ~ 1

Author(s):

Giuseppe Ancona

Keyword(s):

Modular Forms ◽

Shimura Varieties ◽

Manuscripta Math ◽

Modular Surface ◽

Hodge Structures ◽

Picard Modular Forms ◽

Picard Modular Surfaces

We study variations of Hodge structures over a Picard modular surface, and compute the weights and types of their degenerations through the cusps of the Baily–Borel compactification. These computations are one of the key inputs which allow Wildeshaus [On the interior motive of certain Shimura varieties: the case of Picard surfaces, Manuscripta Math. 148(3) (2015) 351–377] to construct motives associated with Picard modular forms.

Download Full-text