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38 votes

Why is differential Galois theory not widely used?

35 votes

What's an example of a transcendental power series?

30 votes
Accepted

How many flat connections has a line bundle in algebraic geometry?

27 votes

Nontrivial theorems with trivial proofs

26 votes

What elementary problems can you solve with schemes?

24 votes
Accepted

Concrete Applications of knowing $\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$

23 votes

What are some famous rejections of correct mathematics?

19 votes

Solving algebraic problems with topology

18 votes
Accepted

applications of Berkovich spaces

18 votes

Covering maps in real life that can be demonstrated to students

17 votes

A slick proof of the Bruhat Decomposition for GL_n(k)?

17 votes
Accepted

What is the precise relationship between o-minimal theory and Grothendieck's "Esquisse d'un programme"?

16 votes
Accepted

An apparent equivalence of the category of affine schemes over $S$ and the category of quasi-coherent $\mathcal{O}_S$-algebras

16 votes

Which nonlinear PDEs are of interest to algebraic geometers and why?

16 votes
Accepted

Algebraic analogue of the Moebius bundle over the circle

16 votes

Math puzzles for dinner

15 votes

Pseudonyms of famous mathematicians

15 votes

What does it mean that $[X]+[Y]=0$ in the Grothendieck ring of varieties?

15 votes
Accepted

Motivation for relative schemes: why should one work with schemes over a ringed topos?

14 votes

Topological characterization of the closed interval $[0,1]$

14 votes

An algebraic number is not a root of unity?

14 votes

Are rational varieties simply connected?

13 votes

What's the "best" proof of quadratic reciprocity?

13 votes
Accepted

About the pro-algebraic group structure of $G(\mathbb{C}[[t]])$

13 votes
Accepted

Analogies between classical geometry on complex surfaces and Arakelov geometry

12 votes

algebraization theorems

12 votes
Accepted

Are there nonobvious cases where equations have finitely many algebraic integer solutions?

12 votes

$\mathbb{P}^n$ is simply connected

12 votes

Are infinite dimensional constructions needed to prove finite dimensional results?

12 votes

Fundamental group as topological group

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