Synthetic spectra and the cellular motivic category

• 成果类型: Article
• 署名作者: Pstragowski, Piotr
• 署名单位: Harvard University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01173-2
• 发表日期: 2023
• 页码: 553-681
• 关键词: homotopy; COHOMOLOGY; quotients; ALGEBRAS

摘要

To an Adams-type homology theory we associate the notion of a synthetic spectrum; this is a product-preserving sheaf on the site of finite spectra with projective E-homology. We show that the infinity-category SynE of synthetic spectra based on E is in a precise sense a deformation of the infinity-category of spectra into quasi-coherent sheaves over a certain algebraic stack, and show that this deformation encodes the E*-based Adams spectral sequence. We describe a symmetric monoidal functor from the infinity-category of cellular motivic spectra over Spec(C) into an even variant of synthetic spectra based on MU and show that it induces an equivalence between the infinity-categories of p-complete objects for all primes p. In particular, it follows that the p-complete cellular motivic category can be described purely in terms of chromatic homotopy theory.