标题： 在椭圆曲线乘积的自同态下横截流形的原像的不可约性准则 显示英文标题

标题： Irreducibility criteria for the preimages of a transverse variety under endomorphisms of products of elliptic curves

摘要： 我们提供了两种不同的证明方法，用于一个不可约性准则，该准则适用于在足够高次数的对角自同态下，乘积椭圆曲线的横截子簇的原像。对于曲线，我们给出了上述不可约性结果的算术证明，这阐明了与Torsion Anomalous Conjecture背景下使用的方法之间的联系。另一方面，我们使用更几何的方法将该结果推广到高维流形。最后，我们给出这些结果的一些应用。更准确地说，我们建立了某些显式多项式族的不可约性，提供了某些交集和像的归一化高度的新估计，并给出了像的本质最小值的新下界。 显示英文摘要

摘要： We provide two different proofs of an irreducibility criterion for the preimages of a transverse subvariety of a product of elliptic curves under a diagonal endomorphism of sufficiently large degree.For curves, we present an arithmetic proof of the aforementioned irreducibility result, which enlightens connections to methods used in the context of the Torsion Anomalous Conjecture. On the other hand, we generalize the result for higher dimensional varieties using a more geometric approach. Finally, we give some applications of these results. More precisely, we establish the irreducibility of some explicit families of polynomials, we provide new estimates for the normalized heights of certain intersections and images, and we give new lower bounds for the essential minima of images.