Dedekind zeta motives for totally real number fields

• 成果类型: Article
• 署名作者: Brown, Francis C. S.
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0444-x
• 发表日期: 2013
• 页码: 257-311
• 关键词: mixed tate motives; hyperbolic manifolds; volumes; polylogarithms; 3-manifolds; COHOMOLOGY

摘要

Let k be a totally real number field. For every odd na parts per thousand yen3, we construct an element in the category MT(k) of mixed Tate motives over k out of the quotient of a product of hyperbolic spaces by an arithmetic group. By a volume calculation, we prove that its period is a rational multiple of , where denotes the special value of the Dedekind zeta function of k. We deduce that the group is generated by the cohomology of a quadric relative to hyperplanes, and that is a determinant of volumes of geodesic hyperbolic simplices defined over k.