Periods of Hodge structures and special values of the gamma function

• 成果类型: Article
• 署名作者: Fresan, Javier
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0690-4
• 发表日期: 2017
• 页码: 247-282
• 关键词: determinant

摘要

At the end of the 1970s, Gross and Deligne conjectured that periods of geometric Hodge structures with multiplication by an abelian number field are products of values of the gamma function at rational arguments, with exponents determined by the Hodge decomposition. We prove an alternating variant of this conjecture for smooth projective varieties acted upon by an automorphism of finite order, thus improving previous results of Maillot and Rossler. The proof relies on a product formula for periods of regular singular connections due to Saito and Terasoma.