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Results tagged with flatness
Search options answers only
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user 6666
10
votes
Accepted
Are irreducible components of a flat family flat?
No to the first question. Let $Y$ be a nodal cubic curve and let $X$ be its connected two-sheeted covering space. Each of the two components of $X$ is the normalization of $Y$.
- 55.9k
2
votes
Accepted
Commutator tensors and submodules
I believe that it holds whenever $A/B$ is flat.
Note (for use in Step 2) that the conclusion can be restated as follows: every element of the kernel of the canonical map $Sym^{n-1}A\otimes B\to Sym^n …
- 55.9k
9
votes
Why did Ravenel define a ring spectrum to be flat if its smash-square splits into copies of ...
I will propose a definition (4) and then discuss what it has to do with (1) and (2).
In algebra an $R$-module is flat if and only if it is a filtered colimit of free $R$-modules. (I don't know how wid …
- 55.9k