English

On ground fields of arithmetic hyperbolic reflection groups. III

Algebraic Geometry 2014-02-26 v3 Geometric Topology

Abstract

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.

Keywords

Cite

@article{arxiv.0710.2340,
  title  = {On ground fields of arithmetic hyperbolic reflection groups. III},
  author = {Viacheslav V. Nikulin},
  journal= {arXiv preprint arXiv:0710.2340},
  year   = {2014}
}

Comments

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

R2 v1 2026-06-21T09:30:43.239Z