This is a survey focusing on the Hasse principle for divisibility of points in commutative
algebraic groups and its relation with the Hasse principle for divisibility of elements of the …

Let ℓ be a prime number. We classify the subgroups G of Sp 4 (F ℓ) and GSp 4 (F ℓ) that act
irreducibly on F ℓ 4, but such that every element of G fixes an F ℓ-vector subspace of …

We provide examples of abelian surfaces over number fields K whose reductions at almost
all good primes possess an isogeny of prime degree ℓ ℓ rational over the residue field, but …

The main topic of this thesis is Galois representations of abelian varieties. Following the
introduction, there are four largely independent chapters that each make progress around …

We say that two abelian varieties $ A $ and $ A'$ defined over a field $ F $ are polyquadratic
twists if they are isogenous over a Galois extension of $ F $ whose Galois group has …

Abstract Hilbert's Tenth Problem (H10) for a ring R asks for an algorithm to decide correctly,
for each f∈ ℤ [X 1,…, X n], whether the diophantine equation f (X 1,…, X n)= 0 has a solution …

We study the rigidity of the local conditions in two well-known local-global principles for
elliptic curves over number fields. In particular, we consider a local-global principle for …

Abstract Let ρ: G→ GL 2 (K) be a continuous representation of a compact group G over a
complete discretely valued field K with ring of integers O and uniformiser π. We prove that tr …

Given an elliptic curve E/k and a Galois extension k/k, we construct an exact functor from
torsion-free modules over the endomorphism ring End Ek with a semilinear Gal (k/k) action …

We study rational points on conic bundles over elliptic curves with positive rank over a
number field. We show that the étale Brauer–Manin obstruction is insufficient to explain …