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.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Inventiones Mathematicae |
| Vol/bind | 230 |
| Sider (fra-til) | 225-319 |
| ISSN | 0020-9910 |
| DOI | |
| Status | Udgivet - 2022 |
Bibliografisk note
Funding Information:
TF was supported by an NSF Graduate Fellowship, a Stanford ARCS Fellowship, and an NSF Postdoctoral Fellowship under grant No. 1902927. SG was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 682922), by the EliteForsk Prize, and by the Danish National Research Foundation (DNRF92 and DNRF151). AV was supported by an NSF DMS grant as well as a Simons investigator grant. SG thanks Andrew Blumberg and Christian Haesemeyer for helpful discussions about K-theory and étale K-theory. All three of us thank the Stanford mathematics department for providing a wonderful working environment.
Publisher Copyright:
© 2022, The Author(s).
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