## Algebraic Groups and Number TheoryThis milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number theory. The exposition of the topic is built on a synthesis of methods from algebraic geometry, number theory, analysis, and topology, and the result is a systematic overview ofalmost all of the major results of the arithmetic theory of algebraic groups obtained to date. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

1 | |

47 | |

Chapter 3 Algebraic Groups over Locally Compact Fields | 107 |

Chapter 4 Arithmetic Groups and Reduction Theory | 171 |

Chapter 5 Adeles | 243 |

Chapter 6 Galois cohomology | 281 |

Chapter 7 Approximation in Algebraic Groups | 399 |

Chapter 8 Class numbers and class groups of algebraic groups | 439 |

Chapter 9 Normal subgroup structure of groups of rational points of algebraic groups | 509 |

Appendix A | 571 |

Appendix B Basic Notation | 579 |

583 | |

609 | |

### Other editions - View all

### Common terms and phrases

abelian adele algebraic groups algebraic number field arbitrary arithmetic groups arithmetic subgroup assertion automorphism Borel subgroup cl(G class number cocycle cohomology commutative completes the proof congruence subgroup conjecture conjugate connected group consider contains Corollary corresponding decomposition defined denote element equivalent exact sequence exists extension L/K finite index finite number finite subset follows fundamental set Gal(L/K Galois extension GLn(R group G groups of type Haar measure Hasse principle hence homomorphism integer involution isomorphism K-group K-group G K-split K-torus kernel lattice Lemma Let G matrix Moreover morphism normal subgroup Note obtain proof of Proposition proof of Theorem prove quadratic extension quadratic form quasisplit reductive respect root satisfying semisimple groups simple simply connected skew field strong approximation subgroup of G suffices suitable surjective theory topology torus trivial unipotent unramified valuation variety weak approximation