2008/11/10 by Benoît Stroh, Stroh, Benoit
Mathematics · #Advanced Algebra and Geometry #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.0811.1484
openalex publication_date 2008/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct the minimal compactification of some modular Siegel varieties at their bad reduction places. These varieties parametrize principally polarized abelian schemes endowed with a parahoric level structure at a prime number p, and with an auxiliary level structure ; such varieties have bad reduction at p. We also sketch the arithmetic theory of the associated Siegel modular forms. ----- Nous construisons la compactification minimale de certaines varietes modulaires de Siegel en leurs places de mauvaise reduction. Ces varietes parametrent des schemas abeliens principalement polarises munis d'une structure de niveau parahorique en un nombre premier p, et d'une structure de niveau auxilliaire ; elles ont mauvaise reduction en p. Nous esquissons egalement une theorie arithmetique des formes modulaires de Siegel associees a ces varietes.