The Galois action on symplectic K-theory

Tony Feng; Soren Galatius; Akshay Venkatesh

doi:10.1007/s00222-022-01127-8

The Galois action on symplectic K-theory

Tony Feng^*, Soren Galatius, Akshay Venkatesh

^*Corresponding author for this work

Department of Mathematical Sciences

Research output: Contribution to journal › Journal article › Research › peer-review

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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 Z_p(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
Journal	Inventiones Mathematicae
Volume	230
Pages (from-to)	225-319
ISSN	0020-9910
DOIs	https://doi.org/10.1007/s00222-022-01127-8
Publication status	Published - 2022

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Publisher Copyright:
© 2022, The Author(s).

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Cite this

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AB - 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.

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