User Arbutus

10 votes

4 answers

2k views

Question about proof that an algebraic integer is a unit if and only if it has norm $\pm 1$.

asked May 25, 2018 at 16:28

10 votes

1 answer

2k views

Prove that $GL_n(\mathbb{F}_p)$ contains an element of order $p^n-1$

asked Jun 22, 2018 at 22:20

8 votes

1 answer

341 views

Are there any nontrivial unramified extensions between two cyclotomic fields?

asked Nov 19, 2019 at 17:49

8 votes

0 answers

188 views

Question on paper of Mazur, Tate, Teitelbaum and $p$-adic L functions of modular forms

asked May 28, 2020 at 14:16

7 votes

1 answer

397 views

Galois action on Tate twist

asked Jan 31, 2020 at 18:39

6 votes

0 answers

362 views

Decomposing the space of modular forms into $\chi$-eigenspaces via representation theory

asked Apr 12, 2019 at 17:25

6 votes

1 answer

908 views

Extending absolute values on local fields - what is the 'correct' normalization and the relation to the global theory?

asked Feb 14, 2019 at 21:58

6 votes

1 answer

626 views

Embedding $\mathbb C_p$ into $\mathbb C$ and vice versa...?

asked Feb 24, 2019 at 14:33

6 votes

1 answer

209 views

Number of roots of a particular polynomial in $F_{121}$

asked Feb 24, 2018 at 23:19

6 votes

1 answer

1k views

Example of a CW complex that is not a $\Delta$-complex?

asked Aug 11, 2018 at 21:14

6 votes

1 answer

523 views

Elliptic curves with supersingular reduction have irreducible mod $p$ representations?

asked Jun 20, 2020 at 18:55

5 votes

1 answer

318 views

Question about proof in Neukirch's Algebraic Number Theory

asked May 14, 2018 at 18:04

4 votes

1 answer

340 views

Ring with finitely many maximal ideals whose localizations are Noetherian injects into $\bigoplus_{\mathfrak{m}}R_{\mathfrak{m}}$

asked Jul 2, 2018 at 20:20

4 votes

2 answers

159 views

If $A,B,C$ are f.g. $\mathbf{Z}/p^n\mathbf{Z}$-modules and $A\oplus C\cong B\oplus C$, show $A\cong B$.

asked Aug 20, 2018 at 0:35

4 votes

2 answers

106 views

Existence of distinct roots of a shifted complex polynomial

asked Mar 5, 2018 at 18:31

4 votes

1 answer

214 views

Understanding the $p$-part of the discriminant of a totally real number field with a single prime above $p$

asked Feb 26, 2019 at 0:17

4 votes

1 answer

142 views

Does there always exist a linear shift of a given polynomial such that all coefficients are nonzero?

asked Mar 6, 2019 at 20:32

4 votes

4 answers

2k views

Showing that $x^2+5=y^3$ has no integer solutions.

asked Jan 25, 2019 at 16:03

4 votes

1 answer

214 views

Where can I find this paper by Iwasawa?

asked Sep 6, 2019 at 14:52

4 votes

1 answer

398 views

Why are $p$-adic characters locally analytic?

asked Aug 28, 2020 at 23:59

4 votes

1 answer

698 views

Residue fields at points on $\mathbb{A}^n$

asked Jun 14, 2020 at 11:56

3 votes

1 answer

335 views

Issue with Hartshorne definition of finite morphism?

asked Jun 11, 2020 at 17:11

3 votes

1 answer

271 views

Is $\mathbb{Q}_p/\mathbb{Z}_p$ an injective $\mathbb{Z}_p$-module?

asked Feb 1, 2020 at 0:25

3 votes

0 answers

66 views

If $A^\Gamma$ is finite why is $A/(\gamma-1)A$ trivial?

asked Feb 5, 2020 at 21:42

3 votes

0 answers

43 views

Quick proof that $SL_2(\mathbb Z/n\mathbb Z)\cong \oplus_{p\mid n}SL_2(\mathbb Z/p^{e_p}\mathbb Z)$

asked Feb 9, 2019 at 19:55

3 votes

1 answer

341 views

Relation between local and global inertia/ramification degrees

asked Nov 5, 2018 at 3:15

3 votes

1 answer

122 views

How to count the number of elements in $(\mathbb{Z}[i]/I^{2014})\otimes_{\mathbb{Z}[i]}(\mathbb{Z}[i]/J^{2014})$?

asked Aug 6, 2018 at 16:58

2 votes

1 answer

122 views

If $K(\alpha)/K$ is Galois and $\exists \sigma\in G$ such that $\sigma \alpha=\alpha^{-1}$, show $[K(\alpha+\alpha^{-1}):K]=\frac{1}{2}[K(\alpha):K]$.

asked Aug 10, 2018 at 20:06

2 votes

1 answer

602 views

Computing the norm of a principal ideal in a quadratic number field

asked May 22, 2018 at 3:48

2 votes

1 answer

463 views

If $f:X\rightarrow X$ is continuous and $(X,d)$ is compact, show there is $\epsilon>0$ such that $d(x,f(x))>\epsilon$ for all $x\in X$.

asked Jan 7, 2019 at 14:26

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50 Questions

Question about proof that an algebraic integer is a unit if and only if it has norm $\pm 1$.

Prove that $GL_n(\mathbb{F}_p)$ contains an element of order $p^n-1$

Are there any nontrivial unramified extensions between two cyclotomic fields?

Question on paper of Mazur, Tate, Teitelbaum and $p$-adic L functions of modular forms

Galois action on Tate twist

Decomposing the space of modular forms into $\chi$-eigenspaces via representation theory

Extending absolute values on local fields - what is the 'correct' normalization and the relation to the global theory?

Embedding $\mathbb C_p$ into $\mathbb C$ and vice versa...?

Number of roots of a particular polynomial in $F_{121}$

Example of a CW complex that is not a $\Delta$-complex?

Elliptic curves with supersingular reduction have irreducible mod $p$ representations?

Question about proof in Neukirch's Algebraic Number Theory

Ring with finitely many maximal ideals whose localizations are Noetherian injects into $\bigoplus_{\mathfrak{m}}R_{\mathfrak{m}}$

If $A,B,C$ are f.g. $\mathbf{Z}/p^n\mathbf{Z}$-modules and $A\oplus C\cong B\oplus C$, show $A\cong B$.

Existence of distinct roots of a shifted complex polynomial

Understanding the $p$-part of the discriminant of a totally real number field with a single prime above $p$

Does there always exist a linear shift of a given polynomial such that all coefficients are nonzero?

Showing that $x^2+5=y^3$ has no integer solutions.

Where can I find this paper by Iwasawa?

Why are $p$-adic characters locally analytic?

Residue fields at points on $\mathbb{A}^n$

Issue with Hartshorne definition of finite morphism?

Is $\mathbb{Q}_p/\mathbb{Z}_p$ an injective $\mathbb{Z}_p$-module?

If $A^\Gamma$ is finite why is $A/(\gamma-1)A$ trivial?

Quick proof that $SL_2(\mathbb Z/n\mathbb Z)\cong \oplus_{p\mid n}SL_2(\mathbb Z/p^{e_p}\mathbb Z)$

Relation between local and global inertia/ramification degrees

How to count the number of elements in $(\mathbb{Z}[i]/I^{2014})\otimes_{\mathbb{Z}[i]}(\mathbb{Z}[i]/J^{2014})$?

If $K(\alpha)/K$ is Galois and $\exists \sigma\in G$ such that $\sigma \alpha=\alpha^{-1}$, show $[K(\alpha+\alpha^{-1}):K]=\frac{1}{2}[K(\alpha):K]$.

Computing the norm of a principal ideal in a quadratic number field

If $f:X\rightarrow X$ is continuous and $(X,d)$ is compact, show there is $\epsilon>0$ such that $d(x,f(x))>\epsilon$ for all $x\in X$.