We describe a family of curves C of genus 2 with a maximal isotropic (Z/5) in J [5], where J is the Jacobian variety of C, and develop the theory required to perform descent via (5, 5)isogeny. We apply this to several examples, where it can shown that non-reducible Jacobians have nontrivial 5-part of the Tate-Shafarevich group.

BACKGROUND Ge/(68)Ga generators provide an inexpensive source of a PET isotope to hospitals without cyclotron facilities. The development of new (68)Ga-based molecular imaging agents and subsequent clinical translation would be greatly facilitated by simplification of radiochemical syntheses. We report the properties of a tris(hydroxypyridinone) conjugate of the SSTR2-targeted peptide, Tyr(3)-o...

We develop a theory of ‘non-abelian higher special elements’ in the non-commutative exterior powers Galois cohomology p-adic representations. explore their relation to organising matrices and thus module structure Selmer modules. In concrete applications, we relate our general formulation refined conjectures Birch Swinnerton-Dyer type Tate–Shafarevich groups abelian varieties.

BACKGROUND 44Sc as a positron emitter can be an interesting alternative to 68Ga (T½=67.71 min) due to its longer half-life (T½=3.97 h). Moreover, the b-emitter 47Sc can be used for therapy when attached to the same biomolecule vectors. DOTA as a chelating agent has been proven suitable for the radiolabelling of peptides recognising tumour cell receptors in vivo with M3+ radiometals. DOTA-deriva...

The geometry of the Lubin-Tate space of deformations of a formal group is studied via anétale, rigid analytic map from the deformation space to projective space. This leads to a simple description of the equivariant canonical bundle of the deformation space which, in turn, yields a formula for the dualizing complex in stable homotopy theory.

In this lecture we introduce a variant of group cohomology known as Tate cohomology, and we define the Herbrand quotient (a ratio of cardinalities of two Tate cohomology groups), which will play a key role in our proof of Artin reciprocity. We begin with a brief review of group cohomology, restricting our attention to the minimum we need to define the Tate cohomology groups we will use. At a nu...