Arithmetic Clifford's theorem for Hermitian vector bundles
Arithmetic cycles on Picard modular surfaces and modular forms of Nebentypus.
Arithmetic differential equations in several variables
We survey recent work on arithmetic analogues of ordinary and partial differential equations.
Arithmetic discriminants and horizontal intersections.
Arithmetic Distance Functions and Height Fuctions in Diophantine Geometry.
Arithmetic Fujita approximation
We prove an arithmetic analogue of Fujita’s approximation theorem in Arakelov geometry, conjectured by Moriwaki, by using measures associated to -filtrations.
Arithmetic genus of integral space curves
We give an estimation for the arithmetic genus of an integral space curve which is not contained in a surface of degree . Our main technique is the Bogomolov-Gieseker type inequality for proved by Macrì.
Arithmetic infinite Grassmannians and the induced central extensions.
Arithmetic intersection theory
Arithmetic models for Hilbert modular varieties
Arithmetic Monodromy Groups.
Arithmetic Normality for Projective Embeddings of Flag Manifolds.
Arithmetic of 0-cycles on varieties defined over number fields
Let be a rationally connected algebraic variety, defined over a number field We find a relation between the arithmetic of rational points on and the arithmetic of zero-cycles. More precisely, we consider the following statements: (1) the Brauer-Manin obstruction is the only obstruction to weak approximation for -rational points on for all finite extensions (2) the Brauer-Manin obstruction is the only obstruction to weak approximation in some sense that we define for zero-cycles of degree...
Arithmetic of cyclic quotients of the Fermat quintic
Arithmetic of formal groups and applications I: Universal norm subgroups.
Arithmetic of Pell surfaces
Arithmetic of the modular function
We find a generator of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.
Arithmetic of Weil Curves.
Arithmetic on certain quadric bundles of relative dimension 2. I.
Arithmetic on Curves of genus 1. VI. The Tate-Safarevic group can be arbitrarily large.