The Galois action on symplectic K-theory

  title={The Galois action on symplectic K-theory},
  author={Tony Feng and S{\o}ren Galatius and Akshay Venkatesh},
  journal={Inventiones mathematicae},
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 $${\mathbf {Q}}$$ 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… 
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