Acyclotomy of torsion in the CM case
Acyclotomy of torsion in the CM case
复制标题
CM 病例中扭转的睫状体切断术
DOI：
10.1007/s11139-020-00271-0
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Marko Milosevic
中科院分区：
文献类型：
--
作者：
Michael Chou;P. L. Clark;Marko Milosevic
Let F be a number field, and let Fcyc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F^{{\text {cyc}}}$$\end{document} be obtained by adjoining to F all the roots of unity. We show that as E ranges over all elliptic curves defined over Fcyc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F^{{\text {cyc}}}$$\end{document} with complex multiplication, the torsion subgroups E(Fcyc)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E(F^{{\text {cyc}}})$$\end{document} are finite and uniformly bounded in size.
Let F be a number field, and let Fcyc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F^{{\text {cyc}}}$$\end{document} be obtained by adjoining to F all the roots of unity. We show that as E ranges over all elliptic curves defined over Fcyc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F^{{\text {cyc}}}$$\end{document} with complex multiplication, the torsion subgroups E(Fcyc)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E(F^{{\text {cyc}}})$$\end{document} are finite and uniformly bounded in size.