Alex Youcis

Berkeley, CA

ayoucis.wordpress.com

Age: 24

I am a second year graduate student at the University of California, Berkeley.

9m
comment Cl(Spec A) = 0 implies A is a UFD
Because how do you define the class group if $A$ isn't regular in codimension one? You also need to know that $A$ is Noetherian.
2h
comment What is the 'Hom-description'?
I'm confused now. Now it does sound like you're talking about thre class group in relation to the zeroth K group, an example of which I mentioned above. What happened to the virtual characters? If $A$ happened to be the maximal order, does $\text{Cl}(A)\oplus\mathbb{Z}=K_0(A)$ fit your need?
2h
comment What is the 'Hom-description'?
Are you aware of the standard way that the class group is a quotient of the idele class group? It's not that, right?
3h
comment What is the 'Hom-description'?
What is the "idels group of $K^c$? So, you want something like $\text{Hom}_{G_K}(R_G,...)$, where that $...$ is whatever the "idels group of $K^c$" is.
3h
comment Best Sets of Lecture Notes and Articles
@Doeser It can be for whoever finds the notes helpful. I've mostly been posting notes I've used over the last four or five years. So, almost none are at standard high school level. But, an advanced high school student may find use in some of them.
3h
comment Best Sets of Lecture Notes and Articles
@Alyosha That's a fair point. Unfortunately, I don't have the time to go through them one-by-one and give a brief description. But, in the future, I will try and give descriptions as I post them.
3h
comment Best Sets of Lecture Notes and Articles
@Doeser Did you read the preamble at all?
4h
revised Best Sets of Lecture Notes and Articles
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4h
comment What is the 'Hom-description'?
I might be able to help if you could give me a better indication of what you're talking about. What type of Hom is this? What are the objects in Hom? etc.
4h
revised Best Sets of Lecture Notes and Articles
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4h
comment Computing the dualizing sheaf of an exceptional divisor
Welcome to the club--we have jackets. :) You might want to answer your own question then, just so this isn't left unanswered!
4h
revised Why is $\text{Mor}_{\mathrm{reg}}(*,W)\to \text{Hom}_{k-\mathrm{alg}}(k[W],k[*])$ not surjective when $W=\mathbb{A}^2\setminus\{(0,0)\}$.
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4h
comment Euler characteristic, genus and cohomology: a deep connection?
@ZhenLin Thanks for saving me from my own spelling mistakes :)
5h
comment What is the 'Hom-description'?
What is $KG$? Is it $K_0(G)$? Are you asking why $K_0(R)=\mathbb{Z}\oplus\text{Cl}(R)$?
5h
comment Alternative proof of Noether Normalization Lemma
I haven't thought through all the details. The hyperplane exists just because it can fit in the complement by dimension arguments. Surjectivity follows because the map is closed, the space is irreducible (you can assume this), and they have the same dimension. So, the image has the same dimension as the domain (by finiteness), and so the same dimension as the codimain, is irreducible and closed, so must be the full thing
5h
comment Computing the dualizing sheaf of an exceptional divisor
Forgive me for asking a silly question, but why doesn't Hartshorne II.8.20 give you this result?
5h
revised Euler characteristic, genus and cohomology: a deep connection?
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5h
answered Euler characteristic, genus and cohomology: a deep connection?
14h
revised How to find a point at a certain distance to other points on the same line
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15h
comment Proof that $A_n$ the only subgroup of $ S_n$ index $2$.
$A_n$ is not always simple. Only for $n\geqslant 5$.
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