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pro vyhledávání: '"Gillibert, Jean"'
It follows from the Grothendieck-Ogg-Shafarevich formula that the rank of an abelian variety (with trivial trace) defined over the function field of a curve is bounded by a quantity which depends on the genus of the base curve and on bad reduction da
Externí odkaz:
http://arxiv.org/abs/2310.01549
We consider elliptic curves defined by an equation of the form $y^2=x^3+f(t)$, where $f\in k[t]$ has coefficients in a perfect field $k$ of characteristic not $2$ or $3$. By performing $2$ and $3$-descent, we obtain, under suitable assumptions on the
Externí odkaz:
http://arxiv.org/abs/2306.11353
Publikováno v:
Proc. Lond. Math. Soc. (3) 127 (2023), no. 1, 134-164
We study the vanishing of Massey products of order at least $3$ for absolutely irreducible smooth projective curves over a perfect field with coefficients in $\mathbb{Z}/\ell$. We mainly focus on elliptic curves, for which we obtain a complete charac
Externí odkaz:
http://arxiv.org/abs/2205.13825
Autor:
Darban, Sina, Jastrzębska, Ilona, Gillibert, Jean, Prorok, Ryszard, Sayet, Thomas, Blond, Eric, Szczerba, Jacek
Publikováno v:
In Journal of the European Ceramic Society September 2024 44(11):6743-6758
Autor:
Gillibert, Jean, Gillibert, Pierre
For each finite subgroup $G$ of $PGL_2(\mathbb{Q})$, and for each integer $n$ coprime to $6$, we construct explicitly infinitely many Galois extensions of $\mathbb{Q}$ with group $G$ and whose ideal class group has $n$-rank at least $\#G-1$. This giv
Externí odkaz:
http://arxiv.org/abs/2005.10920
Publikováno v:
Israel J. Math. 247 (2022), 247, 233-249
We construct \'etale generalized Heisenberg group covers of hyperelliptic curves over number fields. We use these to produce infinite families of quadratic extensions of cyclotomic fields that admit everywhere unramified generalized Heisenberg Galois
Externí odkaz:
http://arxiv.org/abs/1912.03019
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Autor:
Gillibert, Jean, Levin, Aaron
Given a non-isotrivial elliptic curve over $\mathbb{Q}(t)$ with large Mordell-Weil rank, we explain how one can build, for suitable small primes $p$, infinitely many fields of degree $p^2-1$ whose ideal class group has a large $p$-torsion subgroup. A
Externí odkaz:
http://arxiv.org/abs/1811.08166
Autor:
Gillibert, Jean, Levin, Aaron
Publikováno v:
Alg. Number Th. 16 (2022) 311-333
We introduce the use of $p$-descent techniques for elliptic surfaces over a perfect field of characteristic not $2$ or $3$. Under mild hypotheses, we obtain an upper bound for the rank of a non-constant elliptic surface. When $p=2$, this bound is an
Externí odkaz:
http://arxiv.org/abs/1808.08938
Autor:
Gillibert, Jean
Let $C$ be a hyperelliptic curve defined over $\mathbb{Q}$, whose Weierstrass points are defined over extensions of $\mathbb{Q}$ of degree at most three, and at least one of them is rational. Generalizing a result of R. Soleng (in the case of ellipti
Externí odkaz:
http://arxiv.org/abs/1807.02823