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Graduate student trying to learn something.


2d
comment Need a reference book on stokes theorem other than rudin
Lee, smooth manifolds.
Oct
21
comment Hartshorne II prop 6.6
Hey, I read your answer but I am not really understanding, so I will have to spend some more time on this when I have the chance. It's been a long day.
Oct
21
comment Hartshorne II prop 6.6
Hey, thanks for the answer! You've already been a big help on some of my other questions. Its getting late for me but I will be sure to read this carefully tomorrow!
Oct
21
comment Hartshorne II Prop 6.8
@Slade ohh I see, I guess that explains my confusion...
Oct
21
revised Hartshorne II Prop 6.8
deleted 1 character in body
Oct
21
comment Hartshorne II Prop 6.8
I should also note that for 2) it has to be proved that a finite morphism is dominant in this case, which is not trivial, I think. I do have a proof with some help from another grad student.
Oct
21
comment Hartshorne II Prop 6.8
I gave +1 but I still don't completely understand so I can't accept the answer right now. For 1) it isn't clear to me that an integral domain which is a finitely generated $k$-algebra has it's field of fractions a finitely generated $k$-algebra. I also still don't understand 3).
Oct
21
revised Hartshorne II prop 6.6
edited title
Oct
20
accepted Hartshorne Chapter II exercise 5.7 on Invertible sheaves
Oct
20
comment What does “$\mathbb{F^n}$ is a vector space over $\mathbb{F}$” mean?
Have you seen the definition of a vector space yet?
Oct
20
comment Empty function, what is it?
Yeah, specifically the empty relation is a function iff $A$ is empty.
Oct
19
comment boundary value of single complex variable holomorphic function
I don't understand the question. A function holomorphic on the unit disk and continuous on the closure, with value identically zero on the unit circle? Or do you mean something else?
Oct
19
comment For groups and orders show $\forall a,b\in G: |ab|=|ba|$ and $\forall G$ with $|G| = p^n$ for $p$ prime has a subgroup of order $p$
Any element generates a cyclic group. A group is cyclic if it is generated by a single element. There are cyclic groups of every order.
Oct
18
comment Is the range of an injective function dense somewhere?
To be clear, $f$ is not required continuous?
Oct
17
comment Is the plane minus the integer lattice homeomorphic to the plane minus the integers?
What is the fundamental group?
Oct
17
comment how to solve this limit with $e^{x}$
I think if you are going to ask this question you need to tell us exactly how you are defining $e$.
Oct
17
comment Hartshorne II Prop 6.8
I misspoke, I meant finitely generated extension, I understand the difference. However, I don't think that $K(X)$ and $K(Y)$ are a simple extensions of $k$, if they were, wouldn't they be isomorphic since they both have transcendence degree $1$? My understanding is that because $X$ and $Y$ are of dimension $1$, their function fields have transcendence degree $1$ over $k$. But I'm still not clear on why they are finitely generated extensions of $K$. I guess it probably has something to do with $X$ and $Y$ being of finite type over $k$?
Oct
17
comment Hartshorne II Prop 6.8
I appreciate the answer, but you didn't address any of my 3 questions. The first question was, why $K(X)$ is a finite extension of $k$. I apologize if this is trivial, trust me, I already feel stupid asking these questions here, but I'm genuinely stuck on some of this stuff and kind of overwhelmed. Sometimes I can't tell when something is trivial and when it's a theorem I don't know about.
Oct
17
asked Hartshorne II Prop 6.8
Oct
17
comment Hartshorne II prop 6.9
I second that. $ $