The Tate conjecture for surfaces of geometric genus one -- embracing singularities
Abstract
In this article, we aim to largely complete the program of proving the Tate conjecture for surfaces of geometric genus one, by introducing techniques to analyze those surfaces whose "natural models" are singular. As an application, we show that every elliptic curve of height one over a global function field of genus one and characteristic p 11 satisfies the Birch--Swinnerton-Dyer conjecture.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.