The Galois action on symplectic K-theory
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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 language | English |
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Journal | Inventiones Mathematicae |
Volume | 230 |
Pages (from-to) | 225-319 |
ISSN | 0020-9910 |
DOIs | |
Publication status | Published - 2022 |
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© 2022, The Author(s).
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