edoc: No conditions. Results ordered -Date Deposited. 2024-10-11T21:13:54ZEPrintshttps://edoc.unibas.ch/images/uni-logo.jpghttps://edoc.unibas.ch/2020-07-24T13:02:04Z2020-07-24T13:02:04Zhttps://edoc.unibas.ch/id/eprint/59193This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/591932020-07-24T13:02:04ZBounded height in pencils of finitely generated subgroups We prove height bounds concerning intersections of finitely generated subgroups in a torus with algebraic subvarieties, all varying in a pencil. This vastly extends the previously treated constant case and involves entirely different, and more delicate, techniques. Francesco AmorosoDavid MasserUmberto Zannier2019-03-28T09:51:40Z2019-04-20T20:56:12Zhttps://edoc.unibas.ch/id/eprint/69962This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/699622019-03-28T09:51:40ZLower bounds for the height in Galois extensionsWe prove close to sharp lower bounds for the height of an algebraic number in a Galois extension of $\mathbb{Q}$. Francesco AmorosoDavid Masser2012-03-22T13:43:22Z2015-12-31T10:44:59Zhttps://edoc.unibas.ch/id/eprint/8251This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/82512012-03-22T13:43:22ZSmall points on subvarieties of a torusLet V be a subvariety of a torus deﬁned over the algebraic numbers. We give a qualitative and quantitative description of the set of points of V of height bounded by invariants associated to any variety containing V . Especially, we determine whether such a set is or is not dense in V . We then prove that these sets can always be written as the intersection of V with a ﬁnite union of translates of tori of which we control the sum of the degrees. As a consequence, we prove a conjecture by the ﬁrst author and David up to a logarithmic factor. Francesco AmorosoViada Evelina