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 Curious
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2d
asked Does $L_1\oplus\mathbb{A}^1_X\cong L_2\oplus\mathbb{A}^1_X$ imply that $L_1\cong L_2$?
2d
accepted Is taking the product of quasi-projective varieties associative?
Jan
6
asked Is taking the product of quasi-projective varieties associative?
Jan
6
comment Are the quasi-affine subsets of $\mathbb{A}^1_F$ necessarily open or closed?
Ah, I see, the closed sets are the finite ones, or all of $\mathbb{A}^1$. Thanks KReiser, I like the use of a full solution under spoiler text.
Jan
6
accepted Are the quasi-affine subsets of $\mathbb{A}^1_F$ necessarily open or closed?
Nov
12
asked Are the quasi-affine subsets of $\mathbb{A}^1_F$ necessarily open or closed?
Nov
12
revised Are quasiaffine subsets of $\mathbb{A}_F^n$ always necessarily open or closed?
deleted 105 characters in body
Nov
12
comment Are quasiaffine subsets of $\mathbb{A}_F^n$ always necessarily open or closed?
Thanks Slade, sorry I didn't include the definition the first time around. This answer definitely helps.
Nov
12
revised Are quasiaffine subsets of $\mathbb{A}_F^n$ always necessarily open or closed?
added 163 characters in body
Oct
19
asked Are quasiaffine subsets of $\mathbb{A}_F^n$ always necessarily open or closed?
Oct
19
accepted Confused on a proof that $\langle X,1-Y\rangle$ is not principal
Jul
2
awarded  Curious
Apr
10
comment Confused on a proof that $\langle X,1-Y\rangle$ is not principal
Thanks! Is it known that the units of the quotient ring are the same as the units of $\mathbb{Q}[X,Y]$, i.e., just $\mathbb{Q}^\times$? I was working it out, I could only determine that the units are the polynomials $g$ such that there exists $h$, such that $gh-1$ vanishes on the unit circle.
Apr
10
revised Confused on a proof that $\langle X,1-Y\rangle$ is not principal
added 286 characters in body
Apr
9
comment Confused on a proof that $\langle X,1-Y\rangle$ is not principal
May I ask a follow up? If $\langle f^2\rangle=\langle 1-Y\rangle$, doesn't that only imply $f(X,Y)^2g(X,Y)=1-Y$ for some $g(X,Y)$? How can you in fact assume $f(X,Y)^2=1-Y$?
Apr
8
comment Confused on a proof that $\langle X,1-Y\rangle$ is not principal
Thank you Alex.
Apr
8
asked Confused on a proof that $\langle X,1-Y\rangle$ is not principal
Feb
24
comment Equivalent definition of purely inseparable field extension concerning extensions of morphisms.
Thanks Martin. My hypothesis includes that $K/F$ is finite, hence algebraic. So is it correct to conclude that your third paragraph in fact proves the claim in greater generality? Supposing $K/F$ is finite from the start, one could just jump to the last three sentences of your answer, right?
Feb
24
awarded  Critic
Feb
24
asked Equivalent definition of purely inseparable field extension concerning extensions of morphisms.