Nonarchimedean dynamical systems
Non-archimedean intersection indices on projective spaces and the Bruhat-Tits building for
Inspired by Manin’s approach towards a geometric interpretation of Arakelov theory at infinity, we interpret in this paper non-Archimedean local intersection numbers of linear cycles in with the combinatorial geometry of the Bruhat-Tits building associated to .
Non-classical Gorenstein curves of arithmetic genuas three and four.
Non-conservative plane quartic curves in characteristic five.
Non-existence of points rational over number fields on Shimura curves
Jordan, Rotger and de Vera-Piquero proved that Shimura curves have no points rational over imaginary quadratic fields under a certain assumption. In this article, we extend their results to the case of number fields of higher degree. We also give counterexamples to the Hasse principle on Shimura curves.
Non-reflexive curves
Non-solvable base change for Hilbert modular representations and zeta functions of twisted quaternionic Shimura varieties
In this paper we prove some non-solvable base change for Hilbert modular representations, and we use this result to show the meromorphic continuation to the entire complex plane of the zeta functions of some twisted quaternionic Shimura varieties. The zeta functions of the twisted quaternionic Shimura varieties are computed at all places.
Nonstandard arithmetic of function fields over H-convex subfields of *Q.
Non-trivial in the Jacobian of an infinite family of curves of genus 2
We give an infinite family of curves of genus 2 whose Jacobians have non-trivial members of the Tate-Shafarevich group for descent via Richelot isogeny. We prove this by performing a descent via Richelot isogeny and a complete 2-descent on the isogenous Jacobian. We also give an explicit model of an associated family of surfaces which violate the Hasse principle.
Nonvanishing of L-functions and structure of Mordell-Weil groups.
Notes on étale cohomology of number fields
Notes on the arithmetic of Fano threefolds
Notes p-adiques sur les courbes elliptiques.
Null Class Groups of Algebraic Function Fields.
Number of rational places of subfields of the function field of the Deligne-Lusztig curve of Ree type
Numerical characterization of nef arithmetic divisors on arithmetic surfaces
In this paper, we give a numerical characterization of nef arithmetic -Cartier divisors of -type on an arithmetic surface. Namely an arithmetic -Cartier divisor of -type is nef if and only if is pseudo-effective and .
Numerical equivalence and cohomological equivalence for abelian varieties over finite fields. (Equivalence numérique et équivalence cohomologique pour les variétés abéliennes sur les corps finis.)