A. Agboola

On arithmetic class invariants

Let F be a number field with ring of integers OF , and let S be a finite set of places of F . Assume that S contains the set S∞ of archimedean places of F , and write Sf for the set of finite places contained in S. Let OS (or O, when there is no danger of confusion) denote the ring of Sf -integers of F . Write F for an algebraic closure of F . Let Y be any scheme over Spec(O). Suppose thatG is a finite, flat commutative group scheme over Y of exponent N , and let G denote the Cartier dual of G. Let π : X → Y be aG-torsor, and write π0 : G → Y for the trivialG-torsor. ThenOX is anOG-comodule, and so it is also anOGD -module (see [12]). As an OGD -module,OX is locally free of rank one, and it therefore gives a line bundle Mπ over G. Set Lπ := Mπ ⊗M−1 π0 . Then the map ψ : H (Y,G) → Pic(G) ; [π ] → [Lπ ]

Grothendieck Groups of Bundles on Varieties over Finite Fields

Let X be an irreducible, projective variety over a finite field, and let A be a sheaf of rings on X. In this paper, we study Grothendieck groups of categories of vector bundles over certain types of ringed spaces (X, A). Mathematics Subject Classifications (2000): 11-XX, 19-XX, 14-XX, 13-XX.

On Rubin’s variant of the p -adic Birch and Swinnerton-Dyer conjecture

We study Rubins variant of the

On twisted forms and relative algebraic k-theory

p

On Primitive and Realisable Classes

-adic Birch and Swinnerton-Dyer conjecture for CM elliptic curves concerning certain special values of the Katz two-variable

A note on elliptic curves and Galois module structure in global function fields

p

Torsion points on elliptic curves and galois module structure

-adic

Class invariants of Mordell-Weil groups.

L

Line bundles, rational points and ideal classes

-function that lie outside the range of

A geometric description of the class invariant homomorphism

p