Profinite homotopy theory
Profinite homotopy theory
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有限同伦理论
作者：
Gereon Quick
我们构造了一个模型结构上的单纯profinite集，使同伦群进行自然profinite结构。这产生了空间和亲空间的刚性profinite完备函子。一个动机是同伦理论的计划，其中更高的profiniteetale同伦群适合与基本组，这是永远profinite。我们证明了Profi- nitetopological realization函子在几个方面是一个好对象。
We construct a model structure on simplicial profinite sets such that the homotopy groups carry a natural profinite struc- ture. This yields a rigid profinite completion functor for spaces and pro-spaces. One motivation is thehomotopy theory of schemes in which higher profiniteetale homotopy groups fit well with the ´ fundamental group which is always profinite. We show that the profi- nitetopological realization functor is a good object in several respects.