The Galois action on symplectic K-theory

• 成果类型: Article
• 署名作者: Feng, Tony; Galatius, Soren; Venkatesh, Akshay
• 署名单位: University of California System; University of California Berkeley; University of Copenhagen; Institute for Advanced Study - USA
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01127-8
• 发表日期: 2022
• 页码: 225-319
• 关键词: construction; HOMOLOGY

摘要

We study a symplectic variant of algebraic K-theory of the integers, which comes equipped with a canonical action of the absolute Galois group of Q. We compute this action explicitly. The representations we see are extensions of Tate twists Z(p)(2k - 1) by a trivial representation, and we characterize them by a universal property among such extensions. The key tool in the proof is the theory of complex multiplication for abelian varieties.