User Alex Mathers

12 votes

3 answers

4k views

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

asked Jan 4, 2017 at 3:43

11 votes

1 answer

449 views

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

asked Apr 24, 2016 at 20:23

10 votes

1 answer

563 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?

asked Mar 29, 2017 at 18:01

8 votes

1 answer

3k views

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

asked Nov 16, 2015 at 23:04

7 votes

1 answer

196 views

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

asked May 12, 2016 at 23:42

7 votes

0 answers

123 views

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

asked Jul 4, 2017 at 21:53

7 votes

1 answer

500 views

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

asked Jul 9, 2017 at 0:56

7 votes

1 answer

842 views

Showing quasicompactness is affine-local on the target.

asked Jan 15, 2017 at 16:03

7 votes

1 answer

1k views

Proof of the Reduced-to-Separated theorem

asked Feb 3, 2017 at 21:50

7 votes

3 answers

2k views

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

asked Feb 27, 2017 at 13:05

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]

asked Dec 25, 2016 at 17:47

6 votes

1 answer

682 views

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

asked Jul 18, 2017 at 18:34

6 votes

1 answer

366 views

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

asked Jan 30, 2017 at 21:26

6 votes

3 answers

644 views

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

asked May 10, 2016 at 16:54

6 votes

3 answers

399 views

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

asked Apr 26, 2016 at 12:48

5 votes

1 answer

192 views

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

asked Apr 10, 2017 at 17:42

5 votes

1 answer

79 views

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

asked Apr 24, 2017 at 15:53

5 votes

0 answers

342 views

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

asked Aug 21, 2018 at 23:52

5 votes

1 answer

356 views

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

asked Jul 9, 2017 at 3:21

5 votes

1 answer

570 views

Is the zero ideal of a graded ring considered homogeneous?

asked Jan 3, 2017 at 23:28

5 votes

2 answers

591 views

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

asked Jun 2, 2016 at 2:45

5 votes

1 answer

693 views

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

asked Jan 11, 2017 at 6:09

4 votes

1 answer

141 views

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

asked Aug 24, 2018 at 4:48

4 votes

1 answer

631 views

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

asked May 1, 2017 at 23:21

4 votes

1 answer

529 views

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

asked May 2, 2016 at 6:47

4 votes

1 answer

141 views

Why is this not a valid proof?

asked Jun 27, 2015 at 23:37

4 votes

3 answers

518 views

What is common notation for "disjoint union of copies of $\mathbb{R}$"?

asked Jun 27, 2016 at 5:54

4 votes

1 answer

1k views

Noncommutative failure of IBN: $\,R^n\cong R^m \Rightarrow n - m,$ ring $R$ with maximal ideal $I$ such that $R/I$ is not a division ring?

asked Nov 3, 2015 at 4:41

4 votes

1 answer

211 views

Can somebody tell me why this ring homomorphism is invalid?

asked Nov 3, 2015 at 5:50

4 votes

1 answer

2k views

if rank$(T)$=rank$(T^2)$, then $V=R(T)+N(T)$?

asked Sep 23, 2015 at 21:55

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79 Questions

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

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

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?

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

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

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

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

Showing quasicompactness is affine-local on the target.

Proof of the Reduced-to-Separated theorem

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

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

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

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

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

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

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

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

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

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

Is the zero ideal of a graded ring considered homogeneous?

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

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

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

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

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

Why is this not a valid proof?

What is common notation for "disjoint union of copies of $\mathbb{R}$"?

Noncommutative failure of IBN: $\,R^n\cong R^m \Rightarrow n - m,$ ring $R$ with maximal ideal $I$ such that $R/I$ is not a division ring?

Can somebody tell me why this ring homomorphism is invalid?

if rank$(T)$=rank$(T^2)$, then $V=R(T)+N(T)$?