有限环空间的同伦

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2017-10-07 DOI:10.1007/s40062-017-0190-2

Fernando Sancho de Salas

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引用次数: 1

摘要

有限环空间是其底层拓扑空间是有限的环空间。有限环空间的范畴完全包含有限拓扑空间的范畴和仿射格式的范畴。任何环空间，赋以有限开覆盖，产生有限环空间。研究了有限环空间的同伦，将有限拓扑空间的strong同伦分类推广到有限环空间。证明了有限环空间上拟相干模的范畴是同伦不变量。

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Homotopy of finite ringed spaces

A finite ringed space is a ringed space whose underlying topological space is finite. The category of finite ringed spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed space, endowed with a finite open covering, produces a finite ringed space. We study the homotopy of finite ringed spaces, extending Stong’s homotopy classification of finite topological spaces to finite ringed spaces. We also prove that the category of quasi-coherent modules on a finite ringed space is a homotopy invariant.

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来源期刊

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

自引率

0.00%

发文量

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.