论文标题
涂层组
Equivariant sheaves for profinite groups
论文作者
论文摘要
我们研究了涂鸦空间上的模棱两可的滑轮，在该空间中，该组也被视为涂鸦。我们通过使用合适的模棱两可的造型函子来构建良好的模棱两可的预示概念来解决现有理论的严重赤字。使用模棱两可的隔层化，我们开发了一个模块上模块上的层状滑轮的一般理论，提供了无限产物的明确构造，并引入了摩天出式或骨的模拟类似物。 这些结果是作者最近工作的基础，这些工作证明，在涂鸦空间上，有理性G-Spectra的代数模型。该模型是根据g的封闭子组在G的空间上构建的，其中Weyl术语表明H上的茎是H固定的。在本文中，我们证明了R模型的Weyl-G-Sheaves构成了ABELIAN类别，具有足够的注射剂，并且是R-Modules的均衡层的一个核心子类别。 我们以结构性结果结束了论文，该结果提供了另一种方法，可以方便地从更简单的数据中构建均等滑轮。我们证明，在有限的离散空间x_i上，具有有限的g_i的作用，x_i和g是x_i和g的极限是g_i的极限。
We study equivariant sheaves over profinite spaces, where the group is also taken to be profinite. We resolve a serious deficit in the existing theory by constructing a good notion of equivariant presheaves, with a suitable equivariant sheafification functor. Using equivariant sheafification, we develop the general theory of equivariant sheaves of modules over a ring, give explicit constructions of infinite products and introduce an equivariant analogue of skyscraper sheaves. These results underlie recent work by the authors which proves that there is an algebraic model for rational G-spectra in terms of equivariant sheaves over profinite spaces. That model is constructed in terms of Weyl-G-sheaves over the space of closed subgroups of G, where the term Weyl indicates that the stalk over H is H-fixed. In this paper, we prove that Weyl-G-sheaves of R-modules form an abelian category with enough injectives and is a coreflective subcategory of equivariant sheaves of R-modules. We end the paper with a structural result that provides another way to conveniently build equivariant sheaves from simpler data. We prove that a G-equivariant sheaf over a profinite base space X is a colimit of equivariant sheaves over finite discrete spaces X_i with actions of finite groups G_i, where X is the limit of the X_i and G is the limit of the G_i.
