On ground fields of arithmetic hyperbolic reflection groups. III

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

2007-10-11

arxiv.org/abs/0710.2340v3

J. Lond. Math. Soc. (2) 79 (2009), no. 3, 738-756

Mathematics

Algebraic Geometry

Var3: 24 pages, 5 figures; unnecessary Corollary 3.3 removed

Scientific paper

This paper continues arXiv.org:math.AG/0609256, arXiv:0708.3991 and arXiv:0710.0162 . Using authors's methods of 1980, 1981, some explicit finite sets of number fields containing all ground fields of arithmetic hyperbolic reflection groups in dimension at least 3 are defined, and explicit bounds of their degrees (over Q) are obtained. Thus, now, explicit bound of degree of ground fields of arithmetic hyperbolic reflection groups is known in all dimensions. Thus, now, we can, in principle, obtain effective finite classification of arithmetic hyperbolic reflection groups in all dimensions together.

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