This paper describes an intersection theory for arithmetic varieties which generalizes the
work of Arakelov and others on arithmetic surfaces. We develop a theory both of arithmetic …

Using arithmetic intersection theory, a theory of heights for projective varieties over rings of
algebraic integers is developed. These heights are generalizations of those considered by …

We prove in this paper an arithmetic analog of the Riemann-Roch-Grothendieck theorem for
the determinant of the cohomology of an Hermitian vector bundle of arbitrary rank on a …

This book gives a detailed account of recent work on relations between commutative
algebra and intersection theory, with a particular emphasis on applications of the theory of …

In this article, we continue the project we started in [16] of extending Arakelov theory [1],[2] to
higher dimensions. In [16] we defined an intersection theory on arithmetic varieties which …

This book presents an account of several conjectures arising in commutative algebra from
the pioneering work of Serre and Auslander-Buchsbaum. The approach is via Hochster's' …

Let X be a smooth projective Berkovich space over a complete discrete valuation field K of
residue characteristic zero, endowed with an ample line bundle L. We introduce a general …

In this article, we improve our main results from [LL21] in two directions: First, we allow
ramified places in the CM extension at which we consider representations that are spherical …

We define and study the existence of very stable Higgs bundles on Riemann surfaces, how it
implies a precise formula for the multiplicity of the very stable components of the global …

We study the interaction between Fourier-Mukai transforms and perverse filtrations for a
certain class of dualizable abelian fibrations. Multiplicativity of the perverse filtration and the" …