Książka - szczegóły

CONTENTS
Part I
1. Introduction...................................................................................................................................................... 5
2. Preliminaries.................................................................................................................................................. 6
2.1. Notation........................................................................................................................................................ 6
2.2. Local preliminaries.................................................................................................................................... 6
3. The space $\mathscr{A}$............................................................................................................................. 9
3.1. Generalities................................................................................................................................................. 9
3.2. Linear transformations of $\mathscr{A}$............................................................................................... 10
3.3. Global measure.......................................................................................................................................... 11
4. Lattices and convex bodies.......................................................................................................................... 11
4.1. Lattices......................................................................................................................................................... 11
4.2. Convex bodies............................................................................................................................................. 13
5. An analogue of Minkowski's convex body theorem................................................................................. 15
5.1. Convex body theorem................................................................................................................................ 15
5.2. Applications of theorem 2......................................................................................................................... 16
6. Successive minima....................................................................................................................................... 18
6.1. Preliminaries............................................................................................................................................... 18
6.2. The product of successive minima; an upper bound.......................................................................... 19
6.3. The product of successive minima; a lower bound............................................................................ 22
6.4. Applications to algebraic number theory................................................................................................ 24
7. T-adeles........................................................................................................................................................... 32
7.1. The general theory for T-adeles............................................................................................................... 32
7.2. Two special cases..................................................................................................................................... 35
Part II
1. Introduction ..................................................................................................................................................... 37
2. Topology in $\mathscr{G}$................................................................................................................... 37
2.1. Two topologies on $\mathscr{G}$........................................................................................................... 37
2.2. Comparison of the two topologies.......................................................................................................... 39
3. Compactness for lattices............................................................................................................................. 41
3.1. Two topologies on the lattice space....................................................................................................... 41
3.2. An important lemma................................................................................................................................... 43
3.3. An analogue of Mahler’s compactness theorem................................................................................. 44
4. The Chabauty topology................................................................................................................................. 45
5. T-adeles ......................................................................................................................................................... 47
References.......................................................................................................................................................... 49