User Daniel Loughran

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odd degree $0$-cycles and rational points on a quadric hypersurface

answered Sep 9, 2014 at 9:14

5 votes

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Minimal embeddings of certain Fano varieties with Picard number one

answered May 24, 2018 at 7:10

5 votes

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Inert primes in arithmetic progression

answered Sep 25, 2017 at 19:29

5 votes

Dirichlet/Chebotarev's Theorem for natural/analytic density

answered Jun 9, 2018 at 23:29

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Intersection of a line and a conic in a surface

answered Jun 13, 2018 at 11:19

5 votes

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Submersion implies many rational points in image?

answered Oct 2, 2018 at 9:22

5 votes

A property of varieties between unirational and retract rational

answered May 8, 2020 at 18:51

5 votes

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Existence of regular conic bundles with a given discriminant divisor

answered Mar 16, 2017 at 14:30

5 votes

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Density of numbers whose prime factors belong to given arithmetic progressions

answered Mar 21, 2017 at 11:08

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Density of "simultaneous squares"

answered Apr 12, 2017 at 9:34

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Non-rational, smooth Fano 3-folds with $\rho(X) >1$

answered Jul 5, 2017 at 21:07

5 votes

Mordell-Weil rank of some algebraic surface

answered Mar 2, 2022 at 9:31

5 votes

How can the number of rational points depend on the choice of height function?

answered Nov 28, 2020 at 9:34

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An example of a geometrically simply connected variety with infinite Brauer group (modulo constants)

answered Nov 22, 2023 at 10:29

4 votes

Representing $x^6-4$ as a sum of two squares

answered Sep 6, 2023 at 9:15

4 votes

On the Diophantine equation $a^3 + b^3 = c^3 + d^3$

answered Mar 31, 2023 at 19:47

4 votes

Character sums concerning $a^x-1$

answered Feb 18, 2021 at 11:35

4 votes

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Computing $H^1$ with coefficients in a torsion-free abelian group

answered Jul 11, 2021 at 7:59

4 votes

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Hardy-Littlewood circle method for non-diagonal quadratic forms

answered Jul 12, 2021 at 8:17

4 votes

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Chevalley–Warning theorem for rational field $\mathbb{Q} $

answered Aug 10, 2021 at 10:26

4 votes

Variety with two different $\mathrm{mod}\:p$ fibers

answered Sep 16, 2021 at 9:09

4 votes

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Does a smooth relative curve $X/S$ embed into $\mathbb{P}^3_S$?

answered Sep 5, 2022 at 12:25

4 votes

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Irreducible algebraic sets via irreducible polynomials

answered Apr 24, 2016 at 11:39

4 votes

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In what sense can we "describe" the rational points on a unirational surface?

answered Nov 2, 2016 at 15:47

4 votes

Asymptotic formula for the average number of zeros of a polynomial modulo p

answered Dec 11, 2016 at 15:31

4 votes

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Classification of cubic surfaces in $\mathbb{P}^3$

answered Mar 7, 2016 at 21:31

4 votes

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A certain invariant of non-singular algebraic surfaces

answered Jan 12, 2016 at 9:18

4 votes

Applications of the Galois embedding problem

answered Dec 18, 2015 at 9:08

4 votes

Smooth projective surface with geometrically integral reduction

answered Jul 21, 2020 at 14:54

4 votes

Compactification of $PGL(2,\mathbb{C})$

answered Sep 19, 2017 at 17:16

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171 Answers

odd degree $0$-cycles and rational points on a quadric hypersurface

Minimal embeddings of certain Fano varieties with Picard number one

Inert primes in arithmetic progression

Dirichlet/Chebotarev's Theorem for natural/analytic density

Intersection of a line and a conic in a surface

Submersion implies many rational points in image?

A property of varieties between unirational and retract rational

Existence of regular conic bundles with a given discriminant divisor

Density of numbers whose prime factors belong to given arithmetic progressions

Density of "simultaneous squares"

Non-rational, smooth Fano 3-folds with $\rho(X) >1$

Mordell-Weil rank of some algebraic surface

How can the number of rational points depend on the choice of height function?

An example of a geometrically simply connected variety with infinite Brauer group (modulo constants)

Representing $x^6-4$ as a sum of two squares

On the Diophantine equation $a^3 + b^3 = c^3 + d^3$

Character sums concerning $a^x-1$

Computing $H^1$ with coefficients in a torsion-free abelian group

Hardy-Littlewood circle method for non-diagonal quadratic forms

Chevalley–Warning theorem for rational field $\mathbb{Q} $

Variety with two different $\mathrm{mod}\:p$ fibers

Does a smooth relative curve $X/S$ embed into $\mathbb{P}^3_S$?

Irreducible algebraic sets via irreducible polynomials

In what sense can we "describe" the rational points on a unirational surface?

Asymptotic formula for the average number of zeros of a polynomial modulo p

Classification of cubic surfaces in $\mathbb{P}^3$

A certain invariant of non-singular algebraic surfaces

Applications of the Galois embedding problem

Smooth projective surface with geometrically integral reduction

Compactification of $PGL(2,\mathbb{C})$