1,675 research outputs found
Torsion points of abelian varieties with values in infinite extensions over a p-adic field
Let be an abelian variety over a -adic field and an algebraic
infinite extension over . We consider the finiteness of the torsion part of
the group of rational points under some assumptions. In 1975, Hideo Imai
proved that such a group is finite if has good reduction and is the
cyclotomic -extension of . In this talk, first we show a
generalization of Imai's result in the case where has ordinary good
reduction. Next we give some finiteness results when is an elliptic curve
and is the field generated by the -power torsion of an elliptic curve
Invariance of Finiteness of K-area under Surgery
K-area is an invariant for Riemannian manifolds introduced by Gromov as an
obstruction to the existence of positive scalar curvature. However in general
it is difficult to determine whether K-area is finite or not. though the
definition of K-area is quite natural. In this paper, we study how the
invariant changes under surgery.Comment: 8 pages, 0 figure
- …