Author:
Feng Tony,Galatius Soren,Venkatesh Akshay
Abstract
AbstractWe study a symplectic variant of algebraic K-theory 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 $${\mathbf {Z}}_p(2k-1)$$
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.
Funder
Massachusetts Institute of Technology
Publisher
Springer Science and Business Media LLC
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