2016/06/26 by Sudhanshu Shekhar, Shekhar, Sudhanshu
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1606.08034
openalex publication_date 2016/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an abelian variety J and an abelian subvariety A of J over a number\nfield K, we study the visible elements of the Shafarevich-Tate group of A with\nrespect to J over certain number field extension M of K. The notion of visible\nelements in Shafarevich-Tate group of an abelian variety was introduced by\nMazur. In this article, we study the image of Visible elements of A with\nrespect to J under the natural restriction map of the Galois cohomology of A\nover K to the Galois cohomology of A over M. In particular, for a fixed odd\nprime p, we investigate the conditions under which visible elements of order p\ncan be produced over a quadratic extension or a degree p extension M of K.\n