AI 中文总结
本文针对亚当斯猜想的谱变体给出证明，采用F-空间方法建立谱映射的同伦等价，应用刚性Artin-Mazur平展同伦论发展X-纤维化理论，推进了同伦论领域的相关研究。
AI 中文摘要
我们为原亚当斯猜想的谱提供了若干变体的证明。我们的方法使用F-空间（又称Segal Γ-空间），从而建立了与J-映射及亚当斯运算相关的谱映射之间的不稳定与稳定同伦等价。我们采用了适用于正特征域的维特向量上定义的单纯形概形交换图的刚性版本Artin-Mazur平展同伦论。本文大部分内容致力于发展我们所考虑的F-空间上的X-纤维化及l-完全X-纤维化理论。
英文摘要
We provide proofs of several variants for spectra of the original Adams Conjecture. Our approach uses F-spaces (also known as Segal Gamma-spaces), resulting in establishing both unstable and stable homotopy equivalences between maps of spectra associated to the J-map and the Adams operations. We employ a rigid version of Artin-Mazur etale homotopy theory applied to commutative diagrams of simplicial schemes defined over the Witt vectors of fields of positive characteristic. Much of this text is devoting to developing a theory of X-fibrations and l-complete X-fibrations over the F-spaces we consider.
