2024/07/08 by Junaid Hasan, Hasan, Junaid, Hazem Hassan +8 · 1 citation
Mathematics · #14C15 #14K05 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2407.06184
openalex publication_date 2024/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove several results about integral versions of Fourier duality for abelian schemes, making use of Pappas's work on integral Grothendieck-Riemann-Roch. If S is smooth quasi-projective of dimension d over a field and π\colon X→ S is a g-dimensional abelian scheme, we prove, under very mild assumptions on X/S, that all classical results about Fourier duality, including the existence of a Beauville decomposition, are valid for the Chow ring CH(X;Λ) with coefficients in the ring Λ= ℤ[1/(2g+d+1)!]. If X admits a polarization θ of degree ν(θ)2 we further construct an \mathfraksl2-action on CH(X;Λθ) with Λθ= Λ[1/ν(θ)], and we show that CH(X;Λθ) is a sum of copies of the symmetric powers Symn(St) of the 2-dimensional standard representation, for n=0,…,g. For an abelian variety over an algebraically closed field, we use our results to produce torsion classes in CHi(X;Λθ) for every i∈ \1,…,g\.