On fields of definition of arithmetic Kleinian reflection groups
نویسنده
چکیده
We show that degrees of the real fields of definition of arithmetic Kleinian reflection groups are bounded by 35.
منابع مشابه
Finiteness of arithmetic Kleinian reflection groups
We prove that there are only finitely many arithmetic Kleinian maximal reflection groups. Mathematics Subject Classification (2000). Primary 30F40; Secondary 57M.
متن کاملMikhail v. Belolipetsky List of Publications
[1] Estimates for the number of automorphisms of a Riemann surface, Sib. Math. J. 38 (1997), no. 5, 860–867. [2] On Wiman bound for arithmetic Riemann surfaces, with Grzegorz Gromadzki, Glasgow Math. J. 45 (2003), 173–177. [3] Cells and representations of right-angled Coxeter groups, Selecta Math., N. S. 10 (2004), 325–339. [4] On volumes of arithmetic quotients of SO(1,n), Ann. Scuola Norm. Su...
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In [1], Borel discussed discrete arithmetic groups arising from quaternion algebras over number fields with particular reference to arithmetic Kleinian and arithmetic Fuchsian groups. In these cases, he described, in each commensurability class, a class of groups which contains all maximal groups. Developing results on embedding commutative orders of the defining number field into maximal or Ei...
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Using authors’s methods of 1980, 1981, some explicit finite sets of number fields containing ground fields of arithmetic hyperbolic reflection groups are defined, and good bounds of their degrees (over Q) are obtained. For example, degree of the ground field of any arithmetic hyperbolic reflection group in dimension at least 6 is bounded by 56. These results could be important for further class...
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This paper continues [17] (arXiv.org:math.AG/0609256) and [18] (arXiv:0708.3991). Using authors’s methods of 1980, 1981, some explicit finite sets of number fields containing all ground fields of arithmetic hyperbolic reflection groups in dimensions at least 4 are defined, and good explicit bounds of their degrees (over Q) are obtained. This could be important for further classification. Thus, ...
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تاریخ انتشار 2008