There is an algorithm that takes as input a global field k and produces a curve over k violating the local-global principle. Also, given a global field k and a nonnegative integer n, one can effectively construct a curve X over k such that #X(k) = n.National Science Foundation (U.S.) (grant DMS-0841321
International audienceWe show how to transport descent obstructions from the category of covers to t...
Let $E$ be an elliptic curve over a number field $K$. If for almost all primes of $K$, the reduction...
AbstractCounterexamples to the Hasse Principle are constructed for curves of genus 2 to 7. These hav...
A singular curve over a non-perfect field K may not have a smooth model over K. Those are said to ...
We investigate the local-global principle for divisibility by pn in elliptic curves over number fiel...
We prove that the set of rational points on a nonisotrivial curves of genus at least 2 over a global...
In questa tesi viene data una risposta completa alla 4-divisibilita` locale-globale per curve ellitt...
This thesis is concerned with local to global (Hasse) principles in algebraic number theory. We cons...
Let F be a finite field and C, D smooth, geometrically irreducible, proper curves over F and set K ...
Abstract. We conjecture that if C is a curve of genus> 1 over a number field k such that C(k) = ...
We investigate some aspects of the $m$-division field $K({\mathcal{E}}[m])$, where $\mathcal{E}$ is ...
International audienceWe show how to transport descent obstructions from the category of covers to t...
We consider local-global principles for rational points on varieties, in particular torsors, over on...
International audienceWe show how to transport descent obstructions from the category of covers to t...
International audienceWe show how to transport descent obstructions from the category of covers to t...
International audienceWe show how to transport descent obstructions from the category of covers to t...
Let $E$ be an elliptic curve over a number field $K$. If for almost all primes of $K$, the reduction...
AbstractCounterexamples to the Hasse Principle are constructed for curves of genus 2 to 7. These hav...
A singular curve over a non-perfect field K may not have a smooth model over K. Those are said to ...
We investigate the local-global principle for divisibility by pn in elliptic curves over number fiel...
We prove that the set of rational points on a nonisotrivial curves of genus at least 2 over a global...
In questa tesi viene data una risposta completa alla 4-divisibilita` locale-globale per curve ellitt...
This thesis is concerned with local to global (Hasse) principles in algebraic number theory. We cons...
Let F be a finite field and C, D smooth, geometrically irreducible, proper curves over F and set K ...
Abstract. We conjecture that if C is a curve of genus> 1 over a number field k such that C(k) = ...
We investigate some aspects of the $m$-division field $K({\mathcal{E}}[m])$, where $\mathcal{E}$ is ...
International audienceWe show how to transport descent obstructions from the category of covers to t...
We consider local-global principles for rational points on varieties, in particular torsors, over on...
International audienceWe show how to transport descent obstructions from the category of covers to t...
International audienceWe show how to transport descent obstructions from the category of covers to t...
International audienceWe show how to transport descent obstructions from the category of covers to t...
Let $E$ be an elliptic curve over a number field $K$. If for almost all primes of $K$, the reduction...
AbstractCounterexamples to the Hasse Principle are constructed for curves of genus 2 to 7. These hav...
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