picard modular surfaces
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2018 ◽  
Vol 154 (12) ◽  
pp. 2586-2605 ◽  
Author(s):  
Wushi Goldring ◽  
Jean-Stefan Koskivirta

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.


2017 ◽  
Vol 13 (05) ◽  
pp. 1145-1164 ◽  
Author(s):  
Giuseppe Ancona

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.


2013 ◽  
pp. 241-276
Author(s):  
A. Miller ◽  
S. Müller-Stach ◽  
S. Wortmann ◽  
Y.-H. Yang ◽  
K. Zuo

2011 ◽  
Vol 157 (1) ◽  
pp. 239-257 ◽  
Author(s):  
Matthew Stover

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