TITLE

Definable groups and compact p-adic Lie groups

AUTHOR(S)
Onshuus, A.; Pillay, A.
PUB. DATE
August 2008
SOURCE
Journal of the London Mathematical Society;Aug2008, Vol. 78 Issue 1, p233
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We formulate p-adic analogues of the o-minimal group conjectures from the works of Hrushovski, Peterzil and Pillay [J. Amer. Math. Soc., to appear] and Pillay [J. Math. Log. 4 (2004) 147–162]; that is, we formulate versions that are appropriate for groups G definable in (saturated) P-minimal fields. We then restrict our attention to saturated models K of Th(ℚp) and Th(ℚp, an), record some elementary observations when G is defined over the standard model ℚp, and then make a detailed analysis of the case where G = E(K) for E an elliptic curve over K. Essentially, our P-minimal conjectures hold in these contexts and, moreover, our case study of elliptic curves yields counterexamples to a more naive direct translation of the o-minimal conjectures.
ACCESSION #
44398867

 

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