On ground fields of arithmetic hyperbolic reflection groups

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

2007-08-29

arxiv.org/abs/0708.3991v2

CRM Proceedings and Lecture Notes, Vol. 47, (2009), 299 - 326

Mathematics

Algebraic Geometry

Variant 1 is published in Groups and Symmetries, J. Harnad and P. Winternitz (eds.), CRM Proceedings and Lecture Notes, Vol. 4

Scientific paper

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 classification. We also formulate a mirror symmetric conjecture to finiteness of the number of arithmetic hyperbolic reflection groups which was established in full generality recently.

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