User Daniel Loughran

10 votes

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Which abelian varieties over a local field can be globalized?

answered Dec 12 at 17:54

10 votes

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Is there a Chebotarev‘s theorem for non-Galois extension over Q？

answered May 24, 2021 at 9:11

10 votes

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

answered Nov 6, 2018 at 14:36

10 votes

A question on BSD conjecture

answered Aug 31, 2014 at 10:27

10 votes

Geometrically irreducible variety

answered Oct 27, 2015 at 8:52

10 votes

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Picard number and torsion of Neron-Severi group of abelian varieties over a number field

answered May 24, 2011 at 17:26

9 votes

Is there a classification of surface(smooth and projective) over arbitrary field?

answered Feb 26, 2012 at 15:15

9 votes

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Hasse principle and Brauer-Manin obstruction for forms of large degree

answered Apr 10, 2014 at 20:01

9 votes

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Density of multi-grade solutions to $x_1^k+x_2^k+x_3^k = y_1^k+y_2^k+y_3^k$ for $k = 5$ or $6$?

answered Jan 3, 2015 at 15:22

9 votes

Obstruction and rational points on curves

answered Mar 17, 2015 at 8:52

9 votes

What do we know about the number $\prod_p \left( 1 - \frac{1}{p}\right)^4\left( 1 + \frac{4}{p} + \frac{1}{p^2} \right) $?

answered Nov 24, 2017 at 11:40

9 votes

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Elements of arbitrary large order in the first Galois cohomology of an elliptic curve

answered May 21, 2016 at 16:48

9 votes

How many cubes are the sum of three positive cubes?

answered Jan 5, 2022 at 9:34

9 votes

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Does every non-isotrivial 1-parameter family of elliptic curves have a positive rank specialization?

answered Oct 15, 2021 at 11:01

8 votes

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The number of integral solutions to $x^2+y^2-az^2=0$

answered Nov 16, 2015 at 10:47

8 votes

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Automorphisms and infinitesimal deformations of a smooth complete intersection

answered Nov 16, 2015 at 21:10

8 votes

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A sum of divisor functions

answered Jun 8, 2018 at 21:59

8 votes

Are there known cases of the Mumford–Tate conjecture that do not use Abelian varieties?

answered Nov 24, 2014 at 16:54

8 votes

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What is the set of possible densities of pointless members in a family of rational curves over $\mathbb{Q}$?

answered Sep 29, 2013 at 0:14

8 votes

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Parametrization of unit varieties

answered Apr 2, 2011 at 15:03

7 votes

Contour integration of $\zeta(s)\zeta(2s)$

answered Mar 16, 2011 at 10:37

7 votes

Random Diophantine polynomials: Percent solvable?

answered Apr 27, 2015 at 9:07

7 votes

Injectivity under flat base change of the Picard group on smooth projective curves

answered Sep 5, 2014 at 19:40

7 votes

Effective Lang-Weil bounds for del Pezzo surfaces

answered Dec 3, 2018 at 12:35

7 votes

What is the automorphic interpretation of the Weil conjectures over finite fields

answered Oct 24, 2018 at 16:25

7 votes

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Reference request: number of irreducible components and top dimension etale cohomology

answered Sep 19, 2019 at 10:14

7 votes

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Convergence of zeta functions for schemes of finite type over the integers

answered Feb 23, 2016 at 19:10

7 votes

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Obstruction to rationality of del Pezzo surfaces of degree 4

answered May 11, 2016 at 8:33

7 votes

Finite order Hecke characters

answered Aug 1, 2017 at 9:01

7 votes

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Extending rational to integral points

answered Oct 8, 2021 at 17:00

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171 Answers

Which abelian varieties over a local field can be globalized?

Is there a Chebotarev‘s theorem for non-Galois extension over Q？

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

A question on BSD conjecture

Geometrically irreducible variety

Picard number and torsion of Neron-Severi group of abelian varieties over a number field

Is there a classification of surface(smooth and projective) over arbitrary field?

Hasse principle and Brauer-Manin obstruction for forms of large degree

Density of multi-grade solutions to $x_1^k+x_2^k+x_3^k = y_1^k+y_2^k+y_3^k$ for $k = 5$ or $6$?

Obstruction and rational points on curves

What do we know about the number $\prod_p \left( 1 - \frac{1}{p}\right)^4\left( 1 + \frac{4}{p} + \frac{1}{p^2} \right) $?

Elements of arbitrary large order in the first Galois cohomology of an elliptic curve

How many cubes are the sum of three positive cubes?

Does every non-isotrivial 1-parameter family of elliptic curves have a positive rank specialization?

The number of integral solutions to $x^2+y^2-az^2=0$

Automorphisms and infinitesimal deformations of a smooth complete intersection

A sum of divisor functions

Are there known cases of the Mumford–Tate conjecture that do not use Abelian varieties?

What is the set of possible densities of pointless members in a family of rational curves over $\mathbb{Q}$?

Parametrization of unit varieties

Contour integration of $\zeta(s)\zeta(2s)$

Random Diophantine polynomials: Percent solvable?

Injectivity under flat base change of the Picard group on smooth projective curves

Effective Lang-Weil bounds for del Pezzo surfaces

What is the automorphic interpretation of the Weil conjectures over finite fields

Reference request: number of irreducible components and top dimension etale cohomology

Convergence of zeta functions for schemes of finite type over the integers

Obstruction to rationality of del Pezzo surfaces of degree 4

Finite order Hecke characters

Extending rational to integral points