User Daniel Loughran

22 votes

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Simplest diophantine equation with open solvability

answered Mar 8, 2020 at 10:34

19 votes

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"Nearly" Fermat triples: case cubic

answered May 15, 2017 at 9:06

19 votes

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Describe all integer/rational solutions to $x^3+y^3+z^3+t^3+s^3=0$

answered Jul 15, 2023 at 23:16

18 votes

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Anything special (historical?) about surface $x\cdot y\cdot z\ +\ x+y+z=0$?

answered May 24, 2013 at 8:40

18 votes

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Failing of heuristics from circle method

answered Sep 7, 2014 at 17:22

17 votes

number theory which is close to analysis

answered Mar 29, 2015 at 9:16

17 votes

group actions on blow-ups

answered Feb 25, 2013 at 20:46

17 votes

General solution of the quartic $a^4+b^4=c^4+d^4$?

answered Oct 19, 2023 at 20:37

16 votes

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Third Galois cohomology group

answered Jun 1, 2021 at 15:52

14 votes

Building algebraic geometry without prime ideals

answered Dec 2, 2020 at 9:44

14 votes

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On cubic reciprocity for $x^3+y^3+z^3 = 996$?

answered Dec 8, 2015 at 17:24

13 votes

Conics, rational points and probability

answered Dec 23, 2015 at 19:27

13 votes

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Algebraic points of uniformly bounded degree on an algebraic variety

answered May 20, 2016 at 19:01

13 votes

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Albanese variety over non-perfect fields

answered Jan 31, 2017 at 15:47

13 votes

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Smooth proper variety over $\mathbb Q$ with everywhere bad reduction

answered Feb 20, 2019 at 3:47

13 votes

Possible groups of K-rational points for elliptic curves over arbitrary fields

answered Sep 6, 2017 at 11:04

12 votes

A heuristic for the density of solutions to Diophantine equations

answered Jun 21, 2011 at 10:32

12 votes

Polynomial with many integer but no other rational solutions?

answered May 24, 2021 at 15:06

12 votes

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Can you use the delta method for number fields?

answered Sep 5, 2023 at 9:01

11 votes

Has anyone researched additive analogues of toric geometry in characteristic zero?

answered Feb 23, 2023 at 16:23

11 votes

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Embedding torsors of elliptic curves into projective space

answered Nov 23, 2021 at 22:53

11 votes

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Defining isogenies over smaller fields

answered Oct 5, 2012 at 19:09

11 votes

Does every linear group admit a subgroup of dimension 1?

answered Sep 25, 2013 at 21:04

11 votes

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"Forms" of quadrics

answered Sep 23, 2014 at 15:09

11 votes

Proofs of the Chevalley-Warning Theorem

answered Aug 12, 2014 at 7:25

11 votes

Brauer group of a curve over non-algebraically closed field

answered Oct 9, 2018 at 9:35

11 votes

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Reference request: Long exact sequence in profinite Galois cohomology up through $H^2$

answered Oct 23, 2020 at 9:43

11 votes

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What is the density of integers of the form $a^2+nb^2$?

answered Jan 10, 2017 at 8:52

11 votes

Which groups are Galois over some p-adic field?

answered Feb 29, 2016 at 12:09

10 votes

Accepted

Hasse principle and its failure for a special class of plane cubics

answered Nov 6, 2018 at 14:36

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168 Answers

Simplest diophantine equation with open solvability

"Nearly" Fermat triples: case cubic

Describe all integer/rational solutions to $x^3+y^3+z^3+t^3+s^3=0$

Anything special (historical?) about surface $x\cdot y\cdot z\ +\ x+y+z=0$?

Failing of heuristics from circle method

number theory which is close to analysis

group actions on blow-ups

General solution of the quartic $a^4+b^4=c^4+d^4$?

Third Galois cohomology group

Building algebraic geometry without prime ideals

On cubic reciprocity for $x^3+y^3+z^3 = 996$?

Conics, rational points and probability

Algebraic points of uniformly bounded degree on an algebraic variety

Albanese variety over non-perfect fields

Smooth proper variety over $\mathbb Q$ with everywhere bad reduction

Possible groups of K-rational points for elliptic curves over arbitrary fields

A heuristic for the density of solutions to Diophantine equations

Polynomial with many integer but no other rational solutions?

Can you use the delta method for number fields?

Has anyone researched additive analogues of toric geometry in characteristic zero?

Embedding torsors of elliptic curves into projective space

Defining isogenies over smaller fields

Does every linear group admit a subgroup of dimension 1?

"Forms" of quadrics

Proofs of the Chevalley-Warning Theorem

Brauer group of a curve over non-algebraically closed field

Reference request: Long exact sequence in profinite Galois cohomology up through $H^2$

What is the density of integers of the form $a^2+nb^2$?

Which groups are Galois over some p-adic field?

Hasse principle and its failure for a special class of plane cubics