Definable groups and compact p-adic Lie groups

• Autores: Alf Onshuus, Anand Pillay
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 78, Nº 1, 2008, págs. 233-247
• Idioma: inglés
• DOI: 10.1112/jlms/jdn018
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• Resumen

  • 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(p) and Th(p, an), record some elementary observations when G is defined over the standard model p, 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.