Gabriel's user avatar
Gabriel's user avatar
Gabriel's user avatar
Gabriel
  • Member for 9 years, 1 month
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9 votes
Accepted

Categorical definition of Spectrum of a ring as a colimit?

9 votes
Accepted

Proof that $\operatorname{Spec}(\bar{\mathbb{Q}}\otimes_\mathbb{Q} \bar{\mathbb{Q}})\cong\operatorname{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$.

5 votes

Theorem 5.8 Baby Rudin. Some questions

5 votes
Accepted

Can I apply Urysohn's lemma on a locally compact Hausdorff space?

4 votes

Linear algebra: $V$ is the direct sum of $U_1$ and $W$ and of $U_2$ and $W$: are $U_1$ and $U_2$ equal?

4 votes

Localization commutes with arbitrary direct sums

4 votes
Accepted

Why is $k[x,t]/(x^n-t)\simeq k[t]\oplus k[t]\cdot x\oplus\ldots\oplus k[t]\cdot x^{n-1}$ as $k[t]$-modules?

3 votes

About Rudin's outline to proving that Lipschitz functions have converging Fourier Series

3 votes
Accepted

$\text{dim}(\text{Hom}^G(V,W))=1$ implies that isomorphism of representations

3 votes
Accepted

About the functoriality of the long exact sequence in cohomology

2 votes

Translating a diagram chase into an element-free proof

2 votes
Accepted

What is correct representation of homogenous coordinates?

1 vote

Serre quotient category

1 vote

Pushout in an abelian category

1 vote
Accepted

Proof of the exact sequence $0\to H^i(M)\to \operatorname{coker} d^{i-1}\to\ker d^{i+1}\to H^{i+1}(M)\to 0$.

1 vote

Showing the gluability of sheaves

1 vote

Showing that $f^{'} = g$ and that the graph of $D$ is closed

1 vote

How to simplfy this function?

1 vote

The number of solutions of $ax^2+by^2\equiv 1\pmod{p}$ is $ p-\left(\frac{-ab}{p}\right)$

0 votes

Question regarding on powers of a certain matrix

0 votes

Mayer-Vietoris argument to proving that sheaf hom is indeed a sheaf

0 votes

Functoriality in $f$ of the inverse image $f^{-1}\mathscr{F}$ presheaf

0 votes

Is $ R =\{a_{2n} x^{2n} + ... + a_2 x^2 + a_0\mid n \in \Bbb N\}$, subring of $\Bbb Z[x]$, noetherian?

0 votes

Why $A \hookrightarrow B \hookrightarrow C \simeq A$ implies $A \simeq B$?

0 votes

Comparing definitions of smooth and unramified