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

Franck Benoist (1) , Elisabeth Bouscaren (1) , Anand Pillay (2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 UND - University of Notre Dame [Indiana]

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).

Mots clés: socle theorem; Semiabelian variety; Mordell-Lang

Domaines: Logique [math.LO]; Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

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