User Daniel Loughran

23 votes

Accepted

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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Third Galois cohomology group

answered Jun 1, 2021 at 15:52

18 votes

group actions on blow-ups

answered Feb 25, 2013 at 20:46

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

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

answered Oct 19, 2023 at 20:37

14 votes

Building algebraic geometry without prime ideals

answered Dec 2, 2020 at 9:44

14 votes

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Albanese variety over non-perfect fields

answered Jan 31, 2017 at 15:47

14 votes

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

answered Dec 8, 2015 at 17:24

14 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

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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Can you use the delta method for number fields?

answered Sep 5, 2023 at 9:01

13 votes

What is the smallest and "best" 27 lines configuration? And what is its symmetry group?

answered Dec 12 at 14:53

12 votes

Polynomial with many integer but no other rational solutions?

answered May 24, 2021 at 15:06

12 votes

A heuristic for the density of solutions to Diophantine equations

answered Jun 21, 2011 at 10:32

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

Which groups are Galois over some p-adic field?

answered Feb 29, 2016 at 12:09

11 votes

Accepted

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

answered Jan 10, 2017 at 8:52

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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Embedding torsors of elliptic curves into projective space

answered Nov 23, 2021 at 22:53

11 votes

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

answered Feb 23, 2023 at 16:23

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171 Answers

Simplest diophantine equation with open solvability

"Nearly" Fermat triples: case cubic

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

Third Galois cohomology group

group actions on blow-ups

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

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

Building algebraic geometry without prime ideals

Albanese variety over non-perfect fields

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

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

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

Conics, rational points and probability

Algebraic points of uniformly bounded degree on an algebraic variety

Can you use the delta method for number fields?

What is the smallest and "best" 27 lines configuration? And what is its symmetry group?

Polynomial with many integer but no other rational solutions?

A heuristic for the density of solutions to Diophantine equations

Defining isogenies over smaller fields

Does every linear group admit a subgroup of dimension 1?

"Forms" of quadrics

Proofs of the Chevalley-Warning Theorem

Which groups are Galois over some p-adic field?

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

Brauer group of a curve over non-algebraically closed field

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

Embedding torsors of elliptic curves into projective space

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