Definable groups and compact p-adic Lie groups |
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Authors: | Onshuus A; Pillay A |
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Institution: | Departamento de Matemáticas Universidad de Los Andes, AA 4976 Bogotá, DC Colombia |
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Abstract: | We formulate p-adic analogues of the o-minimal group conjecturesfrom 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 groupsG definable in (saturated) P-minimal fields. We then restrictour attention to saturated models K of Th( p) and Th( p, an),record some elementary observations when G is defined over thestandard model p, and then make a detailed analysis of the casewhere 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 toa more naive direct translation of the o-minimal conjectures. |
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