On function field Mordell-Lang: the semiabelian case and the socle theorem

Abstract : In this paper we complete our " second generation " model-theoretic account of the function field Mordell-Lang conjecture, where we avoid appeal to dichotomy theorems for (generalized) Zariski geometries. In the current paper we reduce the semiabelian case to the abelian case using model-theoretic tools. We also use our results from [2] to prove modularity of the " Manin kernels " (over F p (t) sep in positive characterstic and over C(t) alg in characteristic 0).
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Submitted on : Friday, July 28, 2017 - 4:30:27 PM
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  • HAL Id : hal-01469972, version 2
  • ARXIV : 1702.02635

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Franck Benoist, Elisabeth Bouscaren, Anand Pillay. On function field Mordell-Lang: the semiabelian case and the socle theorem. 2017. ⟨hal-01469972v2⟩

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