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508 votes
10 answers
257k views

Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$

110 votes
1 answer
2k views

Tate conjecture for Fermat varieties

  • 4,078
23 votes
3 answers
4k views

Geometrically, why do line bundles have inverses with respect to the tensor product?

  • 5,774
22 votes
1 answer
440 views

Is there any integer solutions of $3x^3+3x+7=y^3$?

10 votes
0 answers
275 views

Quotient Groups and Covering Spaces in Painting Hanging

  • 5,048
9 votes
2 answers
2k views

On $a^4 + b^4 = c^4 + d^4 = e^5$.

8 votes
1 answer
542 views

Name for Theorem 3.27 from baby Rudin?

4 votes
2 answers
215 views

$2^b-1$ does not divide $2^a+1$,how can I show it? [duplicate]

  • 7,483
4 votes
2 answers
1k views

How do ideal quotients behave with respect to localization?

3 votes
0 answers
127 views

Can we view the connected component of the Picard scheme $\text{Pic}_0(X)$ as a "kernel" of the first Chern class?

  • 645
3 votes
0 answers
385 views

K-theory of projective space

  • 645
2 votes
1 answer
601 views

Integral notation for degree homomorphism on algebraic cycles

  • 645
2 votes
1 answer
142 views

$V^* \not\cong V$ if $V$ is infinite-dimensional, problem showing that $\text{Card}(\Lambda \times F) < \text{Card}\left(F^\Lambda\right)$.

  • 5,774
2 votes
0 answers
139 views

Two simple counterexamples in algebraic geometry

  • 645