Qin, Yanshuai (2024) On the Brauer groups of fibrations. MATHEMATISCHE ZEITSCHRIFT, 307 (1): 18. ISSN 0025-5874, 1432-1823
Full text not available from this repository. (Request a copy)Abstract
Let X -> C \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {X}}\rightarrow C$$\end{document} be a flat k-morphism between smooth integral varieties over a finitely generated field k such that the generic fiber X is smooth, projective and geometrically connected. Assuming that C is a curve with function field K, we build a relation between the Tate-Shafarevich group of Pic X / K 0 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textrm{Pic}<^>0_{X/K}$$\end{document} and the geometric Brauer groups of X \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {X}}$$\end{document} and X, generalizing a theorem of Artin and Grothendieck for fibered surfaces to higher relative dimensions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ABELIAN-VARIETIES; TATE-CONJECTURE; K3 SURFACES; FINITENESS THEOREM; NUMBER-FIELDS; SHAFAREVICH; CURVES; Tate conjecture; Brauer group; Tate-Shafarevich group |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Jul 2025 14:25 |
| Last Modified: | 15 Jul 2025 14:25 |
| URI: | https://pred.uni-regensburg.de/id/eprint/63492 |
Actions (login required)
 |
View Item |
