Mariano Suárez-Alvarez
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10h
comment What's the derivative of a map defined on manifolds?
There is no such thing as a derivative of a function $f:M\to\mathbb R$. What there is, though, is a differential of such a function at a point $p\in M$, which is a map $\mathrm d_pf:T_pM\to\mathbb R$. Warner surely tells you what it is!
11h
comment What is the meaning of “B is a bialgebra covariantly acting on A”?
Probably, that $A$ is a $B$-module algebra. One can only guess, thuugh, if you do not provide context.
20h
comment A question regarding Grothendieck , topos and (adelic??) points
You should read, or at least browse, Eisenbud and Harris's book The Geometry of Schemes. They wrote the whole book to answer your question.
20h
comment Grothendiek and singular points
I would say that it has nothing to do with that.
1d
answered Actions of a finite group.
1d
comment Actions of a finite group.
Please add that information to the question itself.
1d
comment Actions of a finite group.
You should make explicit your definition of proper discontinuity; for some variations, this is obvious.
1d
comment Projective objects in BGG category $\mathcal{O}$ are projective $U(\mathfrak{g})$-modules?
Sure. The problem is that the whole category is way too large. $\mathcal O$ is at the same time very small and large enough that it contains lots of modules that are important in nature and exhibits very rich behaviour. That's why it is so significant.
1d
comment Projective objects in BGG category $\mathcal{O}$ are projective $U(\mathfrak{g})$-modules?
$\mathcal O$ is really, really small inside the category of all $U(g)$-modules.
2d
comment What are the prerequisites for Michael Spivak's monumental A Comprehensive Introduction to Differential Geometry?
«To master all the volumes» sounds like a slightly too optimistic idea, regardless of one's command of the prerequesites... It could be argued, too, that it is even a bad plan.
Aug
31
comment Find the series: $\frac{-1}{4}+\left(\frac12+\frac14+\frac28+\frac3{16}+\frac5{32}+\cdots\right)$
What you want is not to find the series (that is easy: it is right there in the title of your question!) but to find the sum of the series.
Aug
31
comment Pentagonal Numbers
The problems in Project Euler are not intended for you to ask for solutions.
Aug
30
revised Show $k[x]\cap(y-x^2,z-x^3)={0}$ in $k[x,y,z]$. $ k$ field.
added 942 characters in body
Aug
30
answered Show $k[x]\cap(y-x^2,z-x^3)={0}$ in $k[x,y,z]$. $ k$ field.
Aug
30
comment Is this called an identity?
It is not that the equation is not true if $x=a$. If $x=a$ then the equation simply does not make sense. Equations that do not make sense are neither true nor false —nor anything else, for that matter!
Aug
30
comment What would the ring $\mathbb{Z}[x,y]/(x^2-y)$ look like?
The second one, at least, has a simple description: the (classes of) the monomials $x^iy^j$ with $i\geq0$ and $0\leq j<2$ is a $\mathbb Z$-basis, and it is easy to describe the product of two of these elements. In other words, it contains the ring $\mathbb Z[x]$ and it is a free module of rank $2$ over it (with $1$ and $y$ as basis, for example)
Aug
30
comment Definition of filtration over monoid
It depends on what that definition is going to be used for, really...
Aug
29
comment What's a somewhat fast introduction to (differential) geometry and algebraic topology for someone who knows a lot of analysis but little else?
Read faster. ${}{}$
Aug
29
comment Is the sphere $S^2$ diffeomorphic to a quotient of the square?
You keep saying that X or Y is diffeomorphic to the square, but that only makes sense if you put a differential structure on the square. It does not have a "standard" one (its standard structure is one with corner, and with it it is most certainly not diffeomorphic to a disc), and you have not said which one you have in mind and, much less, you have bothered to give enough details so that the OP and other people with his question know about it.
Aug
29
comment Is the sphere $S^2$ diffeomorphic to a quotient of the square?
@PaulSinclair, That is only the case if you put on the square a differential structure which already has has the corners smoothed. How to do that is not obvious.