Modularity of formal Fourier--Jacobi series from a cohomological point of view

2024/11/19 by Marco Flores, Flores, Marco · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2411.12691

openalex publication_date 2024/11/19 · openalex created_date 2024/11/21 · openalex updated_date 2026/07/28

Abstract

We investigate the modularity of formal Fourier--Jacobi series by establishing cohomological vanishing results for line bundles defined on compactifications of A_g. Working over ℂ, we show that the minimal compactification of A₂ has only rational singularities, which allows us to characterize, for sufficiently large weights, the modularity of formal Fourier--Jacobi series of genus~2 via cohomological vanishing. Working over ℤ, we introduce a level n≥ 3 structure and, via the the resolution morphism from a toroidal compactification of A_g,n to its minimal compactification, we characterize the modularity of arithmetic formal Fourier--Jacobi series with a level n≥ 3 structure and sufficiently large weight via cohomological vanishing.

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