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Now showing items 1-7 of 7

#### Relative Brauer groups of torsors of period two

(2016)

We consider the problem of computing the relative Brauer group of a torsor of
period two under an elliptic curve. We show how this problem can be reduced to finding a
set of generators for the group of rational points ...

#### Degree and the Brauer-Manin obstruction

(2017)

Let X be a smooth variety over a number field k embedded as a degree d
subvariety of {P}^nk and suppose that X is a counterexample to the
Hasse principle explained by the Brauer-Manin obstruction. We consider the
question ...

#### Improved rank bounds from 2-descent on hyperelliptic Jacobians

(2018)

© 2018 World Scientific Publishing Company. We describe a qualitative improvement to the algorithms for performing 2-descents to obtain information regarding the Mordell-Weil rank of a hyperelliptic Jacobian. The improvement ...

#### Zero-cycles of degree one on Skorobogatov's bielliptic surface

(2017)

© 2017 Elsevier Inc. Skorobogatov constructed a bielliptic surface which is a counterexample to the Hasse principle not explained by the Brauer–Manin obstruction. We show that this surface has a 0-cycle of degree 1, as ...

#### On automorphism groups of toroidal circle planes

(2018)

© 2018, Springer International Publishing AG, part of Springer Nature. Schenkel proved that the automorphism group of a flat Minkowski plane is a Lie group of dimension at most 6 and described planes whose automorphism ...

#### Three-dimensional connected groups of automorphisms of toroidal circle planes

(2018)

We contribute to the classification of toroidal circle planes and flat
Minkowski planes possessing three-dimensional connected groups of
automorphisms. When such a group is an almost simple Lie group, we show that it
is ...

#### Tate-Shafarevich groups of constant elliptic curves and isogeny volcanos

(2019)

We describe the structure of Tate-Shafarevich groups of a constant elliptic curves over function fields by exploiting the volcano structure of isogeny graphs of elliptic curves over finite fields.