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 …

Let i: Y—> X be an embedding of compact complex manifolds. Let r| be a holomorphic vector
bundle on Y and let (0.1)(^): o^-^ _,...-^-. 0 vv be a holomorphic chain complex of vector …

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 …

In this paper, we extend our previous results relating Milnor and Ray-Singer metrics on the
determinant of the cohomology of a flat complex vector bundle to the equivariant case. Thus …

We construct natural Green forms for special cycles in orthogonal and unitary Shimura
varieties, in all codimensions, and, for compact Shimura varieties of type O (p, 2) O (p, 2) and …

The theory of differential characters is developed completely from a de Rham-Federer
viewpoint. Characters are defined as equivalence classes of special currents, called sparks …

In this paper, we introduce an invariant of a K 3 surface with ℤ 2-action equipped with a ℤ 2-
invariant Kähler metric, which we obtain using the equivariant analytic torsion of the trivial …

We consider arithmetic varieties endowed with an action of the group scheme of n-th roots of
unity and we define equivariant arithmetic K 0-theory for these varieties. We use the …

Summary Let i: M′→ M be an immersion of complex manifolds, and let (ζ, ν) be a complex
of holomorphic Hermitian vector bundles on M which provides a projective resolution of the …

K0 (B) ch//CH·(B) Q commutes. Here K0 (Y)(resp. K0 (B)) is the Grothendieck group of locally
free sheaves on Y (resp. on B). The group CH·(Y)(resp. CH·(B)) is the Chow group of cycles …