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Pré-Publication, Document De Travail Année : 2018

AN ABELIAN ANALOGUE OF SCHANUEL'S CONJECTURE AND APPLICATIONS

Biswajyoti Saha
  • Fonction : Auteur
Ekata Saha
  • Fonction : Auteur

Résumé

In this article we study an abelian analogue of Schanuel's conjecture. This conjecture falls in the realm of the generalised period conjecture of Y. André. As shown by C. Bertolin, the generalised period conjecture includes Schanuel's conjecture as a special case. Extending methods of Bertolin, it can be shown that the abelian analogue of Schanuel's conjecture we consider, also follows from André's conjecture. C. Cheng et al. showed that the classical Schanuel's conjecture implies the algebraic independence of the values of the iterated exponential function and the values of the iterated logarithmic function, answering a question of M. Waldschmidt. We then investigate a similar question in the setup of abelian varieties.
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Dates et versions

hal-01918849 , version 1 (12-11-2018)

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Patrice Philippon, Biswajyoti Saha, Ekata Saha. AN ABELIAN ANALOGUE OF SCHANUEL'S CONJECTURE AND APPLICATIONS. 2018. ⟨hal-01918849v1⟩
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