The Galois action on symplectic Ktheory
@article{Feng2022TheGA, title={The Galois action on symplectic Ktheory}, author={Tony Feng and S{\o}ren Galatius and Akshay Venkatesh}, journal={Inventiones mathematicae}, year={2022} }
We study a symplectic variant of algebraic Ktheory of the integers, which comes equipped with a canonical action of the absolute Galois group of $${\mathbf {Q}}$$
Q
. We compute this action explicitly. The representations we see are extensions of Tate twists $${\mathbf {Z}}_p(2k1)$$
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…
One Citation
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