On the growth of torsion in the cohomology of arithmetic groups
On the growth of torsion in the cohomology of arithmetic groups
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算术群上同调中挠率的增长
作者：
Werner Mueller;J. Pfaff
In this paper we consider certain families of arithmetic subgroups of SO0(p,q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{SO }^0(p,q)$$\end{document} and SL3(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{SL }_3(\mathbb {R})$$\end{document}, respectively. We study the cohomology of such arithmetic groups with coefficients in arithmetically defined modules. We show that for natural sequences of such modules the torsion in the cohomology grows exponentially.
In this paper we consider certain families of arithmetic subgroups of SO0(p,q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{SO }^0(p,q)$$\end{document} and SL3(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{SL }_3(\mathbb {R})$$\end{document}, respectively. We study the cohomology of such arithmetic groups with coefficients in arithmetically defined modules. We show that for natural sequences of such modules the torsion in the cohomology grows exponentially.