Timothy Browning:  When is a random Diophantine equation soluble over [...] (NTWS 185)
Channel: Number Theory Web Seminar
Date: 2023-10-23

Title: When is a random Diophantine equation soluble over $\mathbb{Q}_p$ for all $p$?

Abstract:The question in the title is of growing importance in number theory and represents a more tractable staging post than the question of solubility over $\mathbb{Q}$. I'll describe the landscape for various families of varieties, which can be interpreted as a more delicate version of Manin's conjecture, in which one counts rational points of bounded height which lie in the image of adelic points under a  morphism. This leads to more subtle asymptotic behaviours and depends intimately on the geometry of the morphism. This is joint work with Julian Lyczak, Roman Sarapin and Arne Smeets.

Number Theory Web Seminar: https://www.ntwebseminar.org

Original air date: 
Thursday, October 19, 2023 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)Friday, October 20, 2023 (2am AEDT, 4am NZDT)