Manin-Mumford in arithmetic pencils
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Publication:6504517
arXiv2105.12027MaRDI QIDQ6504517
Emmanuel Ullmo, Gregorio Baldi, Rodolphe Richard
Abstract: We obtain a refinement of Manin-Mumford (Raynaud's Theorem) for abelian schemes over some ring of integers. Torsion points are replaced by special 0-cycles, that is reductions modulo some, possibly varying, prime of Galois orbits of torsion points. There is a flat/horizontal part and a vertical one. The irreducible components of the flat part are given by the Zariski closure, over the integers, of torsion cosets of the generic fibre of the abelian scheme. The vertical components are given by translates of abelian subvarieties, which 'come from characteristic zero'.
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