A note on the behaviour of the Tate conjecture under finitely generated field extensions

Autor:	Ambrosi, Emiliano
Rok vydání:	2018
Předmět:	Mathematics - Algebraic Geometry Mathematics - Number Theory
Zdroj:	Pure and Applied Mathematics Quarterly, Vol. 14, No. 3-4 (2018), pp. 515-527
Druh dokumentu:	Working Paper
DOI:	10.4310/PAMQ.2018.v14.n3.a4
Popis:	We show that the $\ell$-adic Tate conjecture for divisors on smooth proper varieties over finitely generated fields of positive characteristic follows from the $\ell$-adic Tate conjecture for divisors on smooth projective surfaces over finite fields. Similar results for cycles of higher co-dimension are given. Comment: v1:6 pages. Comments are welcome. v2: Corrected a gap in the proof of Theorem 1.1.2. Changed Proposition 3.1.2 accordingly. v3: final version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1810.06480 Zobrazit plný text záznamu View this record from Arxiv