Arithmetic intersection on GSpin Rapoport–Zink spaces

On Higher Arithmetic Intersection Theory

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.

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...

On Intersection Sets in Desarguesian Affine Spaces

Lower bounds on the size of t-fold blocking sets with respect to hyperplanes or t-intersection sets in AG(n, q) are obtained, some of which are sharp.

On the Arithmetic Self-intersection Number of the Dualizing Sheaf on Arithmetic Surfaces

We study the arithmetic self-intersection number of the dualizing sheaf on arithmetic surfaces with respect to morphisms of a particular kind. We obtain upper bounds for the arithmetic self-intersection number of the dualizing sheaf on minimal regular models of the modular curves associated with congruence subgroups Γ0(N) with square free level, as well as for the modular curves X(N) and the Fe...