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Results tagged with ac.commutative-algebra
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user 115211
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
5
votes
Accepted
Is a localization of a reduced finitely generated algebra analytically unramified?
Let me expand my comment as an answer. There is a notion of excellent rings, for a precise definition look here https://stacks.math.columbia.edu/tag/07QS (and see Chapter 13 of Matsumura's book "Commu …
- 2,841
5
votes
When does glueing affine schemes produce affine/separated schemes?
There is a general criterion that explains when a gluing of two separated schemes is separated.
Proposition: Let $X_1, X_2$ be a separated $S$-schemes, $U_i$ open subschemes in $X_i$ (for $i=1, 2 …
- 2,841
5
votes
What is the difference between total integral closure and integral closure?
It seems that there is no reference where the notion of total integral closure is discussed in detail. But a good place to look at is Bhatt's notes on perfectoid spaces, especially at Proposition 5.2. …
- 2,841
3
votes
Accepted
Is Frobenius on $R^\circ/p$ surjective for general perfectoid rings $R$?
[Probably this question is no longer interesting to the author. But since I faced the same problem while trying to learn basics of perfectoid spaces I decided to write down an argument here]
We start …
- 2,841
7
votes
1
answer
630
views
Flatness of the integral closure
Let $R$ be a $p$-torsion free ring which is integrally closed in $R[1/p]$ and let $S$ be a finite etale extension of $R[1/p]$.
Is it true that an integral closure $S^+$of $R$ in $S$ is flat over …
- 2,841
8
votes
0
answers
394
views
Foundational Questions on Adic Spaces
There are some foundational questions on adic spaces that I can't find in the literature. It seems that these questions are pretty natural, so I guess that an answer should be known to the experts in …
- 2,841