Geometry of numbers in adele spaces

R. B. McFeat. Geometry of numbers in adele spaces. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1971. <http://eudml.org/doc/268414>.

@book{R1971,
abstract = {CONTENTSPart I1. Introduction...................................................................................................................................................... 52. Preliminaries.................................................................................................................................................. 62.1. Notation........................................................................................................................................................ 62.2. Local preliminaries.................................................................................................................................... 63. The space $\mathcal \{A\}$............................................................................................................................. 93.1. Generalities................................................................................................................................................. 93.2. Linear transformations of $\mathcal \{A\}$............................................................................................... 103.3. Global measure.......................................................................................................................................... 114. Lattices and convex bodies.......................................................................................................................... 114.1. Lattices......................................................................................................................................................... 114.2. Convex bodies............................................................................................................................................. 135. An analogue of Minkowski’s convex body theorem................................................................................. 155.1. Convex body theorem................................................................................................................................ 155.2. Applications of theorem 2......................................................................................................................... 166. Successive minima....................................................................................................................................... 186.1. Preliminaries............................................................................................................................................... 186.2. The product of successive minima; an upper bound.......................................................................... 196.3. The product of successive minima; a lower bound............................................................................ 226.4. Applications to algebraic number theory................................................................................................ 247. T-adeles........................................................................................................................................................... 327.1. The general theory for T-adeles............................................................................................................... 327.2. Two special cases..................................................................................................................................... 35Part II1. Introduction ..................................................................................................................................................... 372. Topology in $\mathcal \{G\}$................................................................................................................... 372.1. Two topologies on $\mathcal \{G\}$........................................................................................................... 372.2. Comparison of the two topologies.......................................................................................................... 393. Compactness for lattices............................................................................................................................. 413.1. Two topologies on the lattice space....................................................................................................... 413.2. An important lemma................................................................................................................................... 433.3. An analogue of Mahler’s compactness theorem................................................................................. 444. The Chabauty topology................................................................................................................................. 455. T-adeles ......................................................................................................................................................... 47References.......................................................................................................................................................... 49},
author = {R. B. McFeat},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Geometry of numbers in adele spaces},
url = {http://eudml.org/doc/268414},
year = {1971},
}

TY - BOOK
AU - R. B. McFeat
TI - Geometry of numbers in adele spaces
PY - 1971
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSPart I1. Introduction...................................................................................................................................................... 52. Preliminaries.................................................................................................................................................. 62.1. Notation........................................................................................................................................................ 62.2. Local preliminaries.................................................................................................................................... 63. The space $\mathcal {A}$............................................................................................................................. 93.1. Generalities................................................................................................................................................. 93.2. Linear transformations of $\mathcal {A}$............................................................................................... 103.3. Global measure.......................................................................................................................................... 114. Lattices and convex bodies.......................................................................................................................... 114.1. Lattices......................................................................................................................................................... 114.2. Convex bodies............................................................................................................................................. 135. An analogue of Minkowski’s convex body theorem................................................................................. 155.1. Convex body theorem................................................................................................................................ 155.2. Applications of theorem 2......................................................................................................................... 166. Successive minima....................................................................................................................................... 186.1. Preliminaries............................................................................................................................................... 186.2. The product of successive minima; an upper bound.......................................................................... 196.3. The product of successive minima; a lower bound............................................................................ 226.4. Applications to algebraic number theory................................................................................................ 247. T-adeles........................................................................................................................................................... 327.1. The general theory for T-adeles............................................................................................................... 327.2. Two special cases..................................................................................................................................... 35Part II1. Introduction ..................................................................................................................................................... 372. Topology in $\mathcal {G}$................................................................................................................... 372.1. Two topologies on $\mathcal {G}$........................................................................................................... 372.2. Comparison of the two topologies.......................................................................................................... 393. Compactness for lattices............................................................................................................................. 413.1. Two topologies on the lattice space....................................................................................................... 413.2. An important lemma................................................................................................................................... 433.3. An analogue of Mahler’s compactness theorem................................................................................. 444. The Chabauty topology................................................................................................................................. 455. T-adeles ......................................................................................................................................................... 47References.......................................................................................................................................................... 49
LA - eng
UR - http://eudml.org/doc/268414
ER -