arXiv subjects

Jean Gillibert

Publications and source records attributed to Jean Gillibert.

28 records · Page 2Linked to original sources

arXiv2014

Category theory, logic and formal linguistics: some connections, old and new

We seize the opportunity of the publication of selected papers from the \emph{Logic, categories, semantics} workshop in the \emph{Journal of Applied Logic} to survey some current trends in logic, namely intuitionistic and linear type theories, that interweave categorical, geometrical and computational considerations. We thereafter present how these rich logical frameworks can model the way language conveys meaning.

math.CT↗

arXiv2013

Analysis of the bending behaviour of flax based reinforcements used in shape forming

The bending behaviour of woven perform was investigated in order to better understand the formation of some defects during sheet forming such as wrinkling and tow buckling. The fabric composition considering hybrid and pure flax fabrics as well as some test conditions like relative humidity were examined. On the one hand, the results show a drop of the bending stiffness with flax/PLA commingled fabric. On the other hand, the study points out that moisture enhances the bending rigidity especially in the case of pure flax fabric. However, an excess of humidity, for instance 100% relative humidity, leads to an opposite effect.

physics.class-ph↗

arXiv2012

Pulling back torsion line bundles to ideal classes

We prove results concerning the specialisation of torsion line bundles on a variety $V$ defined over $\mathbb{Q}$ to ideal classes of number fields. This gives a new general technique for constructing and counting number fields with large class group.

math.NT↗

arXiv2011

The class group pairing and $p$-descent on elliptic curves

We give explicit formulae for the logarithmic class group pairing on an elliptic curve defined over a number field. Then we relate it to the descent relative to a suitable cyclic isogeny. This allows us to connect the resulting Selmer group with the logarithmic class group of the base. These constructions are explicit and suitable for computer experimentation. From a conceptual point of view, the questions that arise here are analogues of "visibility" questions in the sense of Cremona and Mazur.

math.NT↗

arXiv2010

Cohomologie log plate, actions modérées et structures galoisiennes

Let $X$ be a fine and saturated log scheme, and let $G$ be a commutative finite flat group scheme over the underlying scheme of $X$. If $G$-torsors for the fppf topology can be thought of as being unramified objects by nature, then $G$-torsors for the log flat topology allow us to consider tame ramification. Using the results of Kato, we define a concept of Galois structure for these torsors, then we generalize the author's previous constructions (class-invariant homomorphism for semi-stable abelian varieties) in this new setting, thus dropping some restrictions.

math.AG↗

arXiv2009

Prolongement de biextensions et accouplements en cohomologie log plate

We study, using the language of log schemes, the problem of extending biextensions of smooth commutative group schemes by the multiplicative group. This was first considered by Grothendieck in SGA 7. We show that this problem admits a solution in the category of sheaves for Kato's log flat topology, in contradistinction to what can be observed using the fppf topology, for which monodromic obstructions were defined by Grothendieck. In particular, in the case of an abelian variety and its dual, it is possible to extend the Weil biextension to the whole Néron model. This allows us to define a pairing on the points which combines the class group pairing defined by Mazur and Tate and Grothendieck's monodromy pairing.

math.AG↗

arXiv2007

Invariants de classes : propriétés fonctorielles et applications à l'étude du noyau

The class-invariant homomorphism allows one to measure the Galois module structure of torsors--under a finite flat group scheme--which lie in the image of a coboundary map associated to an exact sequence. It has been introduced first by Martin Taylor (the exact sequence being given by an isogeny between abelian schemes). We begin by giving general properties of this homomorphism, then we pursue its study in the case when the exact sequence is given by the multiplication by $n$ on an extension of an abelian scheme by a torus.

math.NT↗

arXiv2007

Invariants de classes : exemples de non-annulation en dimension supérieure

The so-called class-invariant homomorphism $ψ$ measures the Galois module structure of torsors--under a finite flat group scheme $G$--which lie in the image of a coboundary map associated to an isogeny between (Néron models of) abelian varieties with kernel $G$. When the varieties are elliptic curves with semi-stable reduction and the order of $G$ is coprime to 6, is is known that the homomorphism $ψ$ vanishes on torsion points. In this paper, using Weil restrictions of elliptic curves, we give the construction, for any prime number $p>2$, of an abelian variety $A$ of dimension $p$ endowed with an isogeny (with kernel $μ_p$) whose coboundary map is surjective. In the case when $A$ has rank zero and the $p$-part of the Picard group of the base is non-trivial, we obtain examples where $ψ$ does not vanishes on torsion points.

math.NT↗

arXiv2006

Variétés abéliennes et invariants arithmétiques

We define here an analogue, for the Néron model of a semi-stable abelian variety defined over a number field, of M. J. Taylor's class-invariant homomorphism (defined for abelian schemes). Then we extend an annulation result (in the case of an elliptic curve), and an injectivity result regarding an arakelovian version of this homomorphism. This is the sequel to the paper "Invariants de classes : le cas semi-stable".

math.NT↗

arXiv2005

Invariants de classes : le cas semi-stable

We define here an analogue, for a semi-stable group scheme whose generic fiber is an abelian variety, of M. J. Taylor's class-invariant homomorphism (defined for abelian schemes), and we give a geometric description of it. Then we extend a result of Taylor, Srivastav, Agboola and Pappas concerning the kernel of this homomorphism in the case of a semi-stable elliptic curve.

math.NT↗