21 citations · 130 across the 49 of their papers we have counts for
50 papers
Equidistribution theorem over an adelic curve
Huayi Chen, Atsushi Moriwaki
In this article, we introduce the notion of global adelic space of an arithmetic variety over an adelic curve and prove an equidistribution theorem for a generic sequence of subvar…
Hilbert-Samuel formula and positivity over adelic curves
Huayi Chen, Atsushi Moriwaki
We establish, in the setting of Arakelov geometry over adelic curves, an arithmetic Hilbert-Samuel theorem describing the asymptotic behaviour of the metrized graded linear series…
Arithmetic intersection theory over adelic curves
Huayi Chen, Atsushi Moriwaki
We establish an arithmetic intersection theory in the framework of Arakelov geometry over adelic curves. To each projective scheme over an adelic curve, we associate a multi-homoge…
Arakelov theory on arithmetic surfaces over a trivially valued field
Huayi Chen, Atsushi Moriwaki
In this article, we consider an analogue of Arakelov theory of arithmetic surfaces over a trivially valued field. In particular, we establish an arithmetic Hilbert-Samuel theorem a…
Toward Fermat's conjecture over arithmetic function fields
Atsushi Moriwaki
Let K be an arithmetic function field, that is, a field of finite type over the rational number field. In this note, as an application of the height theory due to Chen-Moriwaki, we…
Arakelov geometry over adelic curves
Huayi Chen, Atsushi Moriwaki
The purpose of this book is to build up the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for the researches of arithmetic geometry in…