Relative compactification of semiabelian Néron models, II

2024/05/15 by Iku Nakamura, Nakamura, Iku
Mathematics · Physics and Astronomy · #14K99 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Primary 14K05 #Secondary 14J10

paper · pdf · doi:10.48550/arxiv.2405.09172

openalex publication_date 2024/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a complete discrete valuation ring, k(η) its fraction field, S=\rm Spec R, (G_η,L_η) a polarized abelian variety over k(η) with L_η symmetric ample cubical and G the Néron model of G_η over S. Suppose that G is semiabelian over S. Then there exists a \it unique relative compactification (P,N) of G such that (α) P is Cohen-Macaulay with codim_P(P\setminusG)=2 and (β) N is ample invertible with N_|G cubical and N_η = L^{⊗ n}_η for some positive integer n. The totally degenerate case has been studied in \citeMN24. We discuss here first the partially degenerate case and then the case where R is a Dedekind domain.

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