Daniel Loughran

Bath, UK

https://sites.google.com/site/danielloughran/

I am a lecturer at the University of Bath. I specialise in arithmetic geometry, algebraic number theory and analytic number theory.

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Flatness in Algebraic Geometry vs. Fibration in Topology

ag.algebraic-geometry at.algebraic-topology flatness fibration asked Apr 2, 2010 at 19:47

mathoverflow.net

27 votes

Existence of zero cycles of degree one vs existence of rational points

ag.algebraic-geometry nt.number-theory asked Jul 29, 2010 at 11:47

mathoverflow.net

21 votes

Bounding failures of the integral Hodge and Tate conjectures

ag.algebraic-geometry nt.number-theory arithmetic-geometry hodge-theory asked Jun 4, 2014 at 8:36

mathoverflow.net

21 votes

Class field theory and the class group

nt.number-theory algebraic-number-theory class-field-theory asked Feb 7, 2019 at 10:30

mathoverflow.net

20 votes

Integral points on varieties

ag.algebraic-geometry nt.number-theory asked Jun 17, 2010 at 11:22

mathoverflow.net

19 votes

Finiteness of etale cohomology for arithmetic schemes

ag.algebraic-geometry nt.number-theory arithmetic-geometry etale-cohomology asked Oct 25, 2017 at 11:51

mathoverflow.net

19 votes

Ehresmann's theorem over the $p$-adics

ag.algebraic-geometry nt.number-theory reference-request dg.differential-geometry p-adic-analysis asked Sep 5, 2016 at 10:21

mathoverflow.net

18 votes

Relative Picard functor for the Zariski topology

ag.algebraic-geometry picard-group asked Mar 28, 2015 at 15:50

mathoverflow.net

17 votes

Is a number field uniquely determined by the primes which split in it?

nt.number-theory algebraic-number-theory asked Nov 5, 2014 at 10:16

mathoverflow.net

16 votes

Does every reductive group scheme admit a maximal torus?

ag.algebraic-geometry algebraic-groups group-schemes asked May 2, 2014 at 12:04

mathoverflow.net

Top Answers

Simplest diophantine equation with open solvability

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"Nearly" Fermat triples: case cubic

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

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Failing of heuristics from circle method

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number theory which is close to analysis

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Third Galois cohomology group

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group actions on blow-ups

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

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Building algebraic geometry without prime ideals

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Algebraic points of uniformly bounded degree on an algebraic variety

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Albanese variety over non-perfect fields

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Conics, rational points and probability

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

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A heuristic for the density of solutions to Diophantine equations

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Polynomial with many integer but no other rational solutions?

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

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

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

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Embedding torsors of elliptic curves into projective space

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Defining isogenies over smaller fields

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Which groups are Galois over some p-adic field?

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Does every linear group admit a subgroup of dimension 1?

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

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"Forms" of quadrics

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Proofs of the Chevalley-Warning Theorem

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Brauer group of a curve over non-algebraically closed field

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Geometrically irreducible variety

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A question on BSD conjecture

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

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

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