Serban, Vlad2022-02-282022-02-282022-02-282021-06-0210.1093/imrn/rnab136https://infoscience.epfl.ch/handle/20.500.14299/185768WOS:000755799800001We establish p-adic versions of the Manin-Mumford conjecture, which states that an irreducible subvariety of an abelian variety with dense torsion has to be the translate of a subgroup by a torsion point. We do so in the context of certain rigid analytic spaces and formal groups over a p-adic field or its ring of integers, respectively. In particular, we show that the underlying rigidity results for algebraic functions generalize to suitable p-adic analytic functions. This leads us to uncover purely p-adic Manin-Mumford-type results for formal groups not coming from abelian schemes. Moreover, we observe that a version of the Tate-Voloch conjecture holds: torsion points either lie squarely on a subscheme or are uniformly bounded away from it in the p-adic distance.Mathematicstorsion pointsvarietiestext::journal::journal article::research article