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arXiv · 1811.05167

An abelian analogue of Schanuel's conjecture and applications

Patrice Philippon·Biswajyoti Saha·Ekata Saha
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Abstract

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. Andr{\'e}. 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 Andr{\'e}'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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Patrice Philippon, Biswajyoti Saha, Ekata Saha. 2018-11-13. An abelian analogue of Schanuel's conjecture and applications. https://arxiv.org/abs/1811.05167

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