Automorphic vector bundles with global sections on G-\tt Zip^{\mathcal Z}-schemes

2017/01/02 by Wushi Goldring, Jean-Stefan Koskivirta, Goldring, Wushi +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1701.00333

openalex publication_date 2017/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 A₁ⁿ, C₂ and \mathbf F_p-split groups of type A₂ (this includes all Hilbert-Blumenthal varieties and should also apply to Siegel modular threefolds and Picard modular surfaces). An example is given to show that our conjecture can fail for zip data not of connected-Hodge-type.

Citations

• Torsion in the Coherent Cohomology of Shimura Varieties and Galois Representations
• Generalized mu-ordinary Hasse invariants

Related

• The stack of G-zips is a Mori dream space
• The cone conjecture for vector-valued Siegel automorphic forms
• F-zips with additional structure on splitting models of Shimura varieties
• Divisibility of mod p automorphic forms and the cone conjecture for certain Shimura varieties of Hodge-type
• Purity of G-zips