Titlebook: Arithmetic L-Functions and Differential Geometric Methods; Regulators IV, May 2 Pierre Charollois,Gerard Freixas i Montplet,Vincen Conferen

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Pierre Charollois,Gerard Freixas i Montplet,Vincen

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Two Recent ,-adic Approaches Towards the (Effective) Mordell Conjecture,latter method, which is usually called the method of Chabauty– Kim or non-Abelian Chabauty in the literature, has the advantage that in some cases it has been turned into an effective method to determine the set of rational points on a curve, and we illustrate this by presenting three new examples of modular curves where this set can be determined.

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Analytic Torsion, Regulators and Arithmetic Hyperbolic Manifolds, arithmetic locally symmetric spaces are not compact it is natural to attempt to extend the definition of regulators, and the Cheeger–Müller theorem, to them. We will survey the work of Calegari–Venkatesh, Pfaff and Pfaff together with the author on this topic.

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