Continuity of heights in families and complete intersections in toric varieties

Autor:	Destic, Pablo, Hultberg, Nuno, Szachniewicz, Michał
Rok vydání:	2024
Předmět:	Mathematics - Number Theory Mathematics - Algebraic Geometry Mathematics - Logic 14G40 (Primary) 14M25 52B20 03C66 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We study the variation of heights of cycles in flat families over number fields or, more generally, globally valued fields. To a finite type scheme over a GVF we associate a locally compact Hausdorff space which we refer to as its GVF analytification. For a flat projective family, we prove that the height of fibres is a continuous function on the GVF analytification of the base. As an application, we prove Roberto Gualdi's conjecture on limit heights of complete intersections in toric varieties. Comment: 33 pages, comments welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.15988 Zobrazit plný text záznamu View this record from Arxiv