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Alex Mathers's user avatar
Alex Mathers's user avatar
Alex Mathers
  • Member for 9 years, 2 months
  • Last seen this week
14 votes
3 answers
5k views

Show a scheme is integral if and only if it is irreducible and reduced.

11 votes
1 answer
480 views

Prove that a free group of rank $\ge2$ is centerless and torsion-free

10 votes
1 answer
601 views

Is it possible to find a complex vector bundle on $S^2$ with nonzero first Chern class, which is trivial as a real vector bundle?

9 votes
1 answer
3k views

Show $R$ is right-Artinian but not left-Artinian

8 votes
1 answer
1k views

Proof of the Reduced-to-Separated theorem

7 votes
3 answers
3k views

An orientation-reversing homeomorphism of the circle has two fixed points and rotation number $0$.

7 votes
1 answer
981 views

Showing quasicompactness is affine-local on the target.

7 votes
1 answer
2k views

Show if $f(x+y)=f(x)+f(y)$ for all $x,y$ and $f$ is Lebesgue measurable, then $f$ is continuous. [duplicate]

7 votes
1 answer
700 views

Is the zero ideal of a graded ring considered homogeneous?

7 votes
0 answers
130 views

If $\xi$ is unramified at the valuation $v$, does the associated homogeneous space $C/K$ have a $K_v$-rational point?

7 votes
1 answer
580 views

Showing that the ray class field of $\Bbb Q(i)$ modulo $(2)$ is equal to $\Bbb Q(i)$

7 votes
1 answer
422 views

Definition of the "natural reduction map" $\tilde\phi$ for $\phi:E_1\to E_2$ an isogeny of elliptic curves

7 votes
1 answer
231 views

Is there a rigorous way of saying, "if $G$ and $H$ are isomorphic then $G$ and $H$ share all the same properties"?

6 votes
3 answers
665 views

Why is (one of) the criteria for a Noetherian module not implied by Zorn's lemma?

6 votes
3 answers
471 views

Calculate $\int_0^{\infty}\frac{1}{(x+1)(x-2)}dx$ using residues

6 votes
2 answers
872 views

Correspondence between fractional ideals of $K$ and invertible sheaves of $\operatorname{Spec}\mathcal O_K$.

6 votes
1 answer
384 views

Ramification indices: what does it mean geometrically that $2$ is the only ramified prime in $\Bbb{Z}[i]$?

5 votes
0 answers
412 views

Calculating homology of mapping torus (is this question incorrect?)

5 votes
1 answer
249 views

Calculating the rank of $\widetilde{k[t]/(t)}$ on $Spec(k[t])$

5 votes
1 answer
81 views

Finding $n\dim B$ linearly independent invertible matrices in $M(n,B)$?

5 votes
2 answers
772 views

Show every irreducible subset of a topological space $X$ is contained in a maximal irreducible subset

5 votes
1 answer
866 views

Morphisms $X\to\text{Spec }A$ are in natural bijection with ring morphisms $A\to\Gamma(X,\mathscr O_X)$. [duplicate]

4 votes
1 answer
705 views

Showing the set-theoretic image is contained in the scheme theoretic image.

4 votes
2 answers
599 views

An open subscheme of a variety is a variety?

4 votes
1 answer
777 views

Why are effective divisors the same thing as curves on $X$?

4 votes
1 answer
147 views

Visualizing covers of $S^1\vee S^1$

4 votes
1 answer
148 views

Map $\mathrm{Aut}_X(X_j)\to\mathrm{Aut}_X(X_i)$ in defining fundamental group of a scheme

4 votes
1 answer
395 views

Showing surjectivity of trace map $B\to A$ from faithful flatness

4 votes
1 answer
590 views

If $\sum a_n$ is convergent, is $\sum\frac{a_n}{n}$ absolutely convergent?

4 votes
1 answer
143 views

Why is this not a valid proof?