On ground fields of arithmetic hyperbolic reflection groups. II

Details On ground fields of arithmetic hyperbolic reflection groups. II On ground fields of arithmetic hyperbolic reflection groups. II

2007-09-30

arxiv.org/abs/0710.0162v3

Moscow Math. J. 8 (2008), no.4, 789-812

Mathematics

Algebraic Geometry

Var3: 27 pages, 4 figures; unnecessary Corollary 3.3 removed

Scientific paper

This paper continues arXiv.org:math.AG/0609256 and 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, now, an explicit bound of degree of ground fields of arithmetic hyperbolic reflection groups is unknown in dimension 3 only.

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