On the Discrete Criteria and Jørgensen Inequalities for SL(m, F̅((t)))

Abstract

In this paper, the author gives the discrete criteria and Jørgensen inequalities of subgroups for the special linear group on F̅((t)) in two and higher dimensions.

Keywords

Möbius maps / Discrete criteria / Jørgensen inequalities

References

[1] Armitage J. V., Parker J. R.. Jørgensens inequality for non-archimedean metric spaces. Geometry and Dynamics of Groups and Spaces, 2018, 265: 97-111

[2] Kato F.. Non-archimedean orbifolds covered by Mumford curves. Journal of Algebraic Geometry, 2005, 14: 1-34

[3] Martin G. J.. On discrete Mobius groups in all dimensions: A generalization of Jørgensen’s inequality. Acta Math., 1989, 163: 253-289

[4] Qiu W. Y., Wang Y. F., Yang J. H., Yin Y. C.. On metric properties of limit sets of contractive analytic non-archimedean dynamical systems. J. Math. Anal. Appl., 2014, 414: 386-401

[5] Qiu, W. Y. and Yang, J. H., On limit sets of discontinuous subgroups of the Berkovich space, preprint.

[6] Qiu W. Y., Yang J. H., Yin Y. C.. The discrete subgroups and Jørgensens inequality for SL(m, C_p), Acta Math. Sin.. English Series Mar., 2013, 29(3): 417-428

[7] Wang Y. F., Yang J. H.. The pointwise convergence of the p-adic Möbius maps. Sci. China Math., 2014, 57(1): 1-8

[8] Wang, Y. F. and Yang, J. H., On p-adic Möbius maps. arXiv: 1512.01305.