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Mar
28
comment Projecting an affine hypersurface away from a point in its projective closure is never a finite map?
@user119882 - yup, that's a counterexample! I've edited the question to reflect this.
Mar
27
revised Projecting an affine hypersurface away from a point in its projective closure is never a finite map?
edited the question to engage with user119882's counterexample
Mar
26
comment Schemes to the rescue?
@Jim - when you talk about the scheme-theoretic preimage, I guess you mean the fiber product of the map $x\mapsto x^2$ by the closed embedding of $\mathbb{A}\times 0 \times 0 \times 0\hookrightarrow\mathbb{A}^4$? So this should give a scheme-theoretic description of the pure quaternions. I want a scheme-theoretic description of the conic, so I guess you'd say replace $\mathbb{A}\times 0\times 0\times 0$ with $0\times 0 \times 0\times 0$ and do the same thing?
Mar
26
asked Projecting an affine hypersurface away from a point in its projective closure is never a finite map?
Mar
25
answered First isomorphim theorem $\phi(H) = HN/N$
Mar
20
accepted Discriminant of $f(x^n)$ for $f$ a quadratic
Mar
20
answered Discriminant of $f(x^n)$ for $f$ a quadratic
Mar
19
comment how do you factor $x^2 +kx+40$ over the integer
Do you know what kind of answer is being looked for? Do you get to pick the value of $k$? If so, see if you can find values for the $?$'s so that $(x+\text{first }?)(x+\text{second }?)=x^2 + \text{something} + 40$.
Mar
19
comment how do you factor $x^2 +kx+40$ over the integer
You are correct that $a^2 + 2ab + b^2$ is not applicable since 40 is not a square.
Mar
19
asked How do you compute group cohomology in practice?
Mar
16
awarded  Popular Question
Mar
10
comment Do field automorphisms of a character imply outer automorphisms of the group?
@AlexanderGruber - I believe it is possible for the paper to agree with the claim. If every group (that is not already the outer automorphism group of an abelian simple group) is a homomorphic image of a complete group, then they can both be true.
Mar
10
comment Do field automorphisms of a character imply outer automorphisms of the group?
Aside: a reference for @DerekHolt's claim is Joseph Rotman, An Introduction to the Theory of Groups, Theorem 7.14. (Looking at the 4th edition, this is on pp. 162-163.)
Mar
9
comment Schemes to the rescue?
@FredrikMeyer - I guess the question is how to be confident in a calculation-free way that changes of basis in the quaternion algebra correspond to changes of generators in $k[x,y,z]/(ax^2+by^2 - abz^2)$.
Mar
8
asked Schemes to the rescue?
Mar
8
asked Alias/alibi in permutation groups
Mar
7
comment Lebesgue's Dominated Convergence Theorem questions
Yes, the fact is (B) itself. (A) doesn't imply (B). Davide Giraudo's example 2 illustrates this with $f=0$. Here the functions are going to 0 pointwise, and their integrals are all zero, thus $\lim_n \int f_n = \int f = 0$, but it is not the case that $\lim_n \int |f_n - f| = \lim_n\int |f_n| = 0$.
Mar
3
awarded  Popular Question
Mar
1
accepted Is the completion of $(k[x,y]/f)_\mathfrak{m}$ isomorphic to $k[[x]][y]/f$?
Mar
1
revised $S_6$ contains a subgroup $H$ that is isomorphic to $S_5$ but not conjugate to $S_5$
Added a note glossing "pentad" and "synthemes" for readers unfamiliar with the terms; made a small correction regarding what has been proven