## Geometry of numbers in adele spaces |

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### Contents

Part | 5 |

An analogue of Minkowskis convex body theorem | 15 |

Tadeles | 32 |

2 other sections not shown

### Common terms and phrases

additive quotient topology additive topology adele spaces Ae&T algebraic number theory analogue of Mahler's analogue of Minkowski's B(av body in s/T Cantor Chabauty topology classical geometry compact subset compactness for lattices contains convex body theorem convex distance function corollary to theorem corresponding define definition denote details are given discrete subgroup DISSERTATIONES MATHEMATICAE distinct pairs exist field elements finite follows easily fundamental domain fundamental system geometry of numbers Haar measure Hence idele independent over Q inequalities infinite keZ+ least k distinct lemma linear transformation linearly independent locally compact Mahler's compactness theorem Mahler's theorem mapping metric Minkowski's convex body multiplicative quotient topology multiplicative topology number fields proof of theorem relative topology restricted direct product result satisfy sequence of lattices shape successive minima Suppose symmetric convex body system of neighbourhoods T-adeles T-part topological ring vector space Weiss 16