论文标题
关于Banach戒指光谱的融化特性
On the Sheafyness Property of Spectra of Banach Rings
论文作者
论文摘要
让R为非一切型Banach环，满足我们以后将要指定的一些轻度技术假设。我们证明，可以通过引入衍生有理定位的概念来将同型Huber Spectrum Spa^H（r）关联。如此获得的光谱赋予了简单的Banach代数的衍生结构分层O_ {spa^h（r）}，该代数严格严格是派生的Tate-Cech复合物。在某些假设下，我们可以证明位点spa（r） - > | spa^h（r）|有一个规范的形态。这在一些非透明的巴拉克环的典范中是一个等效性。这也允许使用派生的几何图形工具来理解Spa（R）的几何形状，当时H^0（O_ {Spa（r）}）不是脱节。
Let R be a non-Archimedean Banach ring, satisfying some mild technical hypothesis that we will specify later on. We prove that to R one can associate a homotopical Huber spectrum Spa^h(R) via the introduction of the notion of derived rational localizations. The spectrum so obtained is endowed with a derived structural sheaf O_{Spa^h(R)} of simplicial Banach algebras for which the derived Tate-Cech complex is strictly exact. Under some hypothesis we can prove that there is a canonical morphism of sites Spa(R) -> |Spa^h(R)| that is an equivalence in some well-known examples of non-sheafy Banach rings. This permits to use the tools of derived geometry to understand the geometry of Spa(R) also when H^0(O_{Spa(R)}) is not a sheaf.
