论文标题
对符号$ k $ - 理论的galois行动
The Galois action on symplectic $K$-theory
论文作者
论文摘要
我们研究了代数$ k $ - 整数理论的符合性变体，该变体配备了$ \ mathbf {q} $的绝对Galois组的规范动作。我们明确计算此操作。我们看到的表示是TATE TWIST的扩展$ \ Mathbf {z} _p（2k-1）$通过微不足道的表示，我们通过此类扩展中的通用属性来表征它们。 证明的关键工具是阿贝尔品种的复杂乘法理论。
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 $\mathbf{Q}$. We compute this action explicitly. The representations we see are extensions of Tate twists $\mathbf{Z}_p(2k-1)$ 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.
