On Tate’s Acyclicity and uniformity of Berkovich spectra and adic spectra
On Tate’s Acyclicity and uniformity of Berkovich spectra and adic spectra
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伯科维奇谱和adic谱的塔特无环性和均匀性
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发表时间：
2014
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通讯作者：
Tomoki Mihara
中科院分区：
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作者：
Tomoki Mihara
我们构造了一个非sheafy均匀Banach代数，使得合理的局部化的Berkovich谱不保持均匀性。我们还构造了罗兰Huber意义上的均匀仿射环，使得进谱的有理局部化不保持均匀性。其中之一是一个例子的非sheafy均匀仿射环。我们引入了局部一致性的概念，并证明了局部一致性蕴涵层条件。
We construct a non-sheafy uniform Banach algebra such that a rational localisation of the Berkovich spectrum does not preserve the uniformity. We also construct uniform affinoid rings in the sense of Roland Huber such that rational localisations of the adic spectra do not preserve the uniformity. One of them is an example of a non-sheafy uniform affinoid ring. We introduce the notion of local uniformity instead, and prove that the local uniformity implies the sheaf condition.