  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.

Algebraic Geometry;Geometric Topology