Path-Connected Components of Affine Schemes and Algebraic K-Theory
| Autor: | Sadr, Maysam Maysami |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | We introduce a functor $\mathfrak{M}:\mathbf{Alg}\times\mathbf{Alg}^\mathrm{op}\rightarrow\mathrm{pro}\text{-}\mathbf{Alg}$ constructed from representations of $\mathrm{Hom}_\mathbf{Alg}(A,B\otimes ? )$. As applications, the following items are introduced and studied: (i) Analogue of the functor $\pi_0$ for algebras and affine schemes. (ii) Cotype of Weibel's concept of strict homotopization. (iii) A homotopy invariant intrinsic singular cohomology theory for affine schemes with cup product. (iv) Some extensions of $\mathbf{Alg}$ that are enriched over idempotent semigroups. (v) Classifying homotopy pro-algebras for Corti\~{n}as-Thom's KK-groups and Weibel's homotopy K-groups. Comment: 37 pages. The author would like to express his sincere gratitude to Professor Cortinas for many valuable comments, hints, and remarks on the early version of this manuscript |
| Databáze: | arXiv |
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