Arithmetic intersection theory

On Higher Arithmetic Intersection Theory

Capacity Theory and Arithmetic Intersection Theory

We show that the sectional capacity of an adelic subset of a projective variety over a number field is a quasi-canonical limit of arithmetic top self-intersection numbers, and we establish the functorial properties of extremal plurisubharmonic Green’s functions. We also present a conjecture that the sectional capacity should be a top selfintersection number in an appropriate adelic arithmetic i...

Arithmetic Intersection Theory on Deligne-mumford Stacks

In this paper the arithmetic Chow groups and their product structure are extended from the category of regular arithmetic varieties to regular Deligne-Mumford stacks proper over a general arithmetic ring. The method used also gives another construction of the product on the usual Chow groups of a regular Deligne-Mumford stack.

Computing canonical heights using arithmetic intersection theory

The canonical height ĥ on an abelian variety A defined over a global field k is an object of fundamental importance in the study of the arithmetic of A. For many applications it is required to compute ĥ(P ) for a given point P ∈ A(k). For instance, given generators of a subgroup of the Mordell-Weil group A(k) of finite index, this is necessary for most known approaches to the computation of gen...

Arithmetic Intersection Theory on Flag Varieties

Let F be the complete flag variety over SpecZ with the tautological filtration 0 ⊂ E1 ⊂ E2 ⊂ · · · ⊂ En = E of the trivial bundle E over F . The trivial hermitian metric on E(C) induces metrics on the quotient line bundles Li(C). Let ĉ1(Li) be the first Chern class of Li in the arithmetic Chow ring ĈH(F ) and x̂i = −ĉ1(Li). Let h∈Z[X1, . . . , Xn] be a polynomial in the ideal 〈e1, . . . , en〉 ge...