Related papers: Torseurs arithmetiques et espaces fibres
Let R be a Henselian discrete valuation ring with field of fractions K. If X is a smooth variety over K and G a torus over K, then we consider X-torsors under G. If XX/R is a model of X then, using a result of Brahm, we show that X-torsors…
Semi-arithmetic Fuchsian groups is a wide class of discrete groups of isometries of the hyperbolic plane which includes arithmetic Fuchsian groups, hyperbolic triangle groups, groups admitting a modular embedding, and others. We introduce a…
The purpose of this paper is to give a linear and effective height inequality for algebraic points on curves over functional fields. Our height inequality can be viewed as the logarithmic canonical class inequality of a punctured curve over…
In this paper, we propose a new height function for a variety defined over a finitely generated field over Q. For this height function, we will prove Northcott's theorem and Bogomolov's conjecture, so that we can recover the original…
We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the sum with respect to…
We define a new height function on rational points of a DM (Deligne-Mumford) stack over a number field. This generalizes a generalized discriminant of Ellenberg-Venkatesh, the height function recently introduced by…
We give a survey of analytic and geometric results on `fibred cusp spaces', a large class of non-compact Riemannian manifolds which include the regular parts of singular spaces with incomplete cusp singularities as well as complete spaces…
We prove that the number of rational points of bounded height on certain del Pezzo surfaces of degree 1 defined over Q grows linearly, as predicted by Manin's conjecture. Along the way, we investigate the average number of integral points…
Several recent papers construct auxiliary polynomials to bound the Weil height of certain classes of algebraic numbers from below. Following these techniques, the author gave a general method for introducing auxiliary polynomials to…
The structural connectome is often represented by fiber bundles generated from various types of tractography. We propose a method of analyzing connectomes by representing them as a Riemannian metric, thereby viewing them as points in an…
We give a mathematical structure on an arithmetic surface, that has algebraic meanings over finite places and can estimate the canonical norm for a relative differential form on the arithmetic surface. This will give a lower bound for the…
In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particular care to establish a notion of smooth variation of such…
Many interesting classes of maps from homotopical algebra can be characterised as those maps with the right lifting property against certain sets of maps (such classes are sometimes referred to as cofibrantly generated). In a more…
This paper has two goals. The first is to present the construction, due to the author, of measures on non-archimedean analytic varieties associated to metrized line bundles and some of its applications. We take this opportunity to add…
In this note we define fibrations of topological stacks and establish their main properties. We prove various standard results about fibrations (fiber homotopy exact sequence, Leray-Serre and Eilenberg-Moore spectral sequences, etc.). We…
We study the behaviour of analytic torsion under smooth fibrations. Namely, let F \to E \to^{f} B be a smooth fiber bundle of connected closed oriented smooth manifolds and let $V$ be a flat vector bundle over $E$. Assume that $E$ and $B$…
In algebraic geometry there is the notion of a height pairing of algebraic cycles, which lies at the confluence of arithmetic, Hodge theory and topology. After explaining a motivating example situation, we introduce new directions in this…
A system of transformations is associated to a rational point on an elliptic curve. The sequence entropy is connected to the canonical height, and in some cases there is a canonically defined quotient system whose entropy is the canonical…
Torsors under affine groups are generalized in the super context by super-torsors under affine super-groups. We investigate those super-torsors by using Hopf-algebra language and techniques. It is explicitly shown, under suitable…
Recently, R\'emond stated a very general conjecture on lower bounds of a normalized height on either an abelian variety or a power of the multiplicative group. In this note, we extend a particular case of this conjecture to split…