Recent progress on the Tate conjecture

2017/06/16 by Burt Totaro · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Coding theory and cryptography #Analytic Number Theory Research #Conjecture #Mathematics #Algebraic number #Hodge conjecture #Collatz conjecture #Algebraic geometry #Pure mathematics #Algebraic surface #Algebraic cycle #Beal's conjecture #Algebra over a field #Hodge theory #Mathematical analysis

paper · pdf · doi:10.1090/bull/1588

openalex publication_date 2017/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07

Abstract

We survey the history of the Tate conjecture on algebraic cycles. The conjecture is closely related with other big problems in arithmetic and algebraic geometry, including the Hodge and Birch–Swinnerton-Dyer conjectures. We conclude by discussing the recent proof of the Tate conjecture for K3 surfaces over finite fields.

Citations

• The Tate conjecture for K3 surfaces in odd characteristic
• Endlichkeitss�tze f�r abelsche Variet�ten �ber Zahlk�rpern
• Notes on elliptic curves. II.
• 2-adic integral canonical models and the Tate conjecture in characteristic 2
• Arithmetic Geometry

Cited by

• Tate conjecture [wikipedia]

Related

• Building bridges between Tate conjectures and arithmetic invariants
• The Tate Conjecture for Motivic Endomorphisms of K3 Surfaces over Finite Fields
• The Tate conjecture over finite fields (AIM talk)
• An approach to the Tate conjecture for surfaces over a finite field
• A survey around the Hodge, Tate and Mumford-Tate conjectures for abelian varieties