Generalized Campana points and adelic approximation on toric varieties

Autor:	Moerman, Boaz
Rok vydání:	2024
Předmět:	Mathematics - Algebraic Geometry Mathematics - Number Theory 14G12 (Primary) 14M25 14G05 11G35 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We introduce a general framework for studying special subsets of rational points on an algebraic variety, termed $\mathcal{M}$-points. The notion of $\mathcal{M}$-points generalizes the concepts of integral points, Campana points and Darmon points. We introduce and study $M$-approximation over number fields and function fields, which is a notion that generalizes weak and strong approximation. We show that this property implies that the set of $\mathcal{M}$-points is not thin. We then give a simple characterisation of when a split toric variety satisfies $M$-approximation, generalizing work of Nakahara and Streeter. Further, we determine when the set of $\mathcal{M}$-points on a split toric variety is thin. Comment: 70 pages; Corollary 4.21 added, minor other changes
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.03048 Zobrazit plný text záznamu View this record from Arxiv