Mariano Suárez-Alvarez
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3h
comment Exercise about an algebraic surface
Is the intersection of four smooth quadrics in $P^6$ automatically smooth?
1d
comment Find an arbitrary power of a lower triangular matrix of size $3\times 3$
This is a trivial matter using induction, really. I doubt there is any gain going in any other route...
1d
comment Why should statistics be considered mathematics?
What does «being together» even mean?
2d
answered Is parallel transport injective?
May
23
comment In (relatively) simple words: What is an inverse limit?
@AsafKaragila the claim that diagrams never help is uncharacteristically absurd coming from you...
May
22
comment simplicial homology definition
'\mathring\Delta' gives $\mathring\Delta$
May
22
comment Equivalence between category of $R$-modules and $S$-modules
@MartinBrandenburg, of course it is wrong. There do exist isomorphisms. Can you give an example relevant to this question?
May
22
comment If $M\bigoplus N $ submodule $A\bigoplus B$ does it imply either $M$ submodule $A$ or $M$ submodule $ B$
If it seems «very obvious» you should declare example hunting season started, for your intuition needs series adjusting!
May
22
answered Equivalence between category of $R$-modules and $S$-modules
May
22
comment Equivalence between category of $R$-modules and $S$-modules
One would usually only consider equivalences, as isomorphisms of categories are mostly nonexistent in nature — and then the rings need not be isomorphic; the keyword for this is «Morita equivalence».
May
22
comment What are Products and Quotients of vector space used for?
"Done Right" does not include giving a motivation!?
May
21
comment When does covering preserve rational cohomology?
Having tangent bundle with zero Pontriagin classes, for example, is a property of smooth manifolds which is a topological condition, and that is a significant theorem — and its significance, of course, is, precisely that there is a non-trivial content in claiming that a condition on the tangent bundle is topological.
May
21
comment When does covering preserve rational cohomology?
Well it is a rather inconvenient terminology when it is inconvenient. As I mentioned, there are homeomorphic smooth manifolds with non-isomorphic tangent bundles, so it is quite conceivable that there exist pairs of manifolds which are homeomorphic and of which exactly one has trivial tangent bundle. In that case, «has trivial tangent bundle» could only very weirdly be called a topological condition.
May
21
comment Regular subrings of a polynomial ring
By first sentence refers to the version f your question before the last edit: it claimed that if $D$ is a f.g. algebra such that $\mathbb C\subseteq D\subseteq\mathbb C[x_1,\dots,x_]$ and which is regular, then the fraction field of $D$ coincides with that of $\mathbb C[x_1,\dots,x_]$. This is false, as an example I mentioned many comments ago shows. You probably did not mean to write that but you did. :-)
May
21
comment Dimension of Conjugacy class in $SU(n)$
Well the orbit, as a manifold, is the quotient of the group by the centralizer, so you can figure out the dimension easily then!
May
21
comment Dimension of Conjugacy class in $SU(n)$
Of course. ${}{}$
May
21
comment Dimension of Conjugacy class in $SU(n)$
Can you compute the dimension of the centralizer?
May
21
comment When does covering preserve rational cohomology?
The triviality of a tangent bunde is a topological condition? There exist pairs of homeomorphic non diffeomorphic smooth manifolds with non isomorphic tangeent bundles, at least math.stackexchange.com/questions/469992/…
May
20
comment Correspondence between Ext group and extensions (from Weibel's book)
Well, it would be good if the question were understandable without having the book at hand. It currently isn't :-)
May
20
comment Correspondence between Ext group and extensions (from Weibel's book)
You seem to have left out some details in the statement of the theorem. For example, what is $M$?