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1d
comment Projective curve $x^d+y^d+z^d=0$ is nonsingular using Jacobian matrix
I can't believe I missed this. Thank you for taking the time to write an answer.
1d
accepted Projective curve $x^d+y^d+z^d=0$ is nonsingular using Jacobian matrix
2d
asked Projective curve $x^d+y^d+z^d=0$ is nonsingular using Jacobian matrix
2d
comment Quotient of local ring is of finite length
Youngsu, zcn Thank you both. Yes this is what I had in mind. Feel free to post an answer and I'll accept.
Aug
17
comment Completion of quotient of polynomial ring
@RghtHndSd I used $\hat{A_\mathfrak{m}}\cong\hat{A}$ where $\mathfrak{m}$ is a maximal ideal of the Noetherian ring $A $. Seems to do the trick.
Aug
17
accepted Completion of quotient of polynomial ring
Aug
17
comment Quotient of local ring is of finite length
@user26857 I checked those answers. Thanks for that. This answer is similar to mine, but uses a result related to nonzero divisors in Noetherian rings. I'm not familiar with that. My argument doesn't use such a result. My question is whether my argument is correct or not.
Aug
17
asked Quotient of local ring is of finite length
Aug
16
comment Completion of quotient of polynomial ring
Thank you. I guess you mean $R=k[x,y]_{(x,y)}$ and $f=xy$. How do we know that the completion of $k[x,y]_{(x,y)}$ is $k[[x,y]]$?
Aug
16
asked Completion of quotient of polynomial ring
Aug
16
comment Cardinality of variety
@RobertAuffarth I didn't know about the geometric statement of this lemma. It looks like it can be used indeed.
Aug
16
revised Cardinality of variety
deleted 367 characters in body
Aug
16
accepted Definition of degree of commutative ring $d(A) $ based on Hilbert polynomial
Aug
16
comment Definition of degree of commutative ring $d(A) $ based on Hilbert polynomial
I confused $ A / {m}^{n}$ with $m^{n }/ m^ {n +1}$. Thank you
Aug
15
awarded  Yearling
Aug
11
accepted Unique line through two points in projective space
Aug
11
asked Definition of degree of commutative ring $d(A) $ based on Hilbert polynomial
Aug
11
accepted Canonical isomorphism between Cauchy sequence completion and inverse limit
Aug
5
comment Canonical isomorphism between Cauchy sequence completion and inverse limit
@ThomasAndrews It is a neighbourhood system, so every open neighbourhood of $ 0 $ must contain one of $ G_{i} $. This neighbourhood system is transported to other points of $ G$ via the homeomorphisms $x \mapsto x + a$.
Aug
5
comment Canonical isomorphism between Cauchy sequence completion and inverse limit
@ThomasAndrews Edited my question and added the definition.