Galois equivariance and stable motivic homotopy theory
Galois equivariance and stable motivic homotopy theory
复制标题
伽罗瓦等变性和稳定动机同伦理论
DOI：
10.1090/tran6647
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发表时间：
2014
影响因子：
1.3
通讯作者：
K. Ormsby
中科院分区：
文献类型：
--
作者：
J. Heller;J. Heller;K. Ormsby
对于具有Galois群G的域L/k的有限Galois扩张，我们研究了由经典Galois对应诱导的从G-等变稳定同伦范畴到k上稳定动机同伦范畴的函子.我们证明了在素数和η(Motivic Hopf映射)处完成之后，当k是实闭的且L=k[i]时，这将导致一个完全且忠实的嵌入。如果Serre有限定理的一个动机版本是有效的，则它是在η-完成之后的完全且忠实的嵌入。我们在域扩张L/k上给出了这个函子满的、忠实的必要条件。在此过程中，我们得到了关于稳定的C2-等变Betti实现函子的几个结果，并证明了p-初等C2-等变Adams谱序列的收敛定理。
For a finite Galois extension of fields L/k with Galois group G, we study a functor from the G-equivariant stable homotopy category to the stable motivic homotopy category over k induced by the classical Galois correspondence. We show that after completing at a prime and η (the motivic Hopf map) this results in a full and faithful embedding whenever k is real closed and L = k[i]. It is a full and faithful embedding after η-completion if a motivic version of Serre’s finiteness theorem is valid. We produce strong necessary conditions on the field extension L/k for this functor to be full and faithful. Along the way, we produce several results on the stable C2-equivariant Betti realization functor and prove convergence theorems for the p-primary C2-equivariant Adams spectral sequence.