The Galois action on symplectic K-theory

Tony Feng*, Soren Galatius, Akshay Venkatesh

*Corresponding author for this work

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Abstract

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 Zp(2 k- 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.

Original languageEnglish
JournalInventiones Mathematicae
Volume230
Pages (from-to)225-319
ISSN0020-9910
DOIs
Publication statusPublished - 2022

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