## Adeles and algebraic groups |

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### Contents

PRELIMINARIES ON ADELEGEOMETRY | 1 |

TAMAGAWA MEASURES | 10 |

THE LINEAR PROJECTIVE AND SYMPLECTIC GROUPS | 30 |

Copyright | |

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### Common terms and phrases

absolutely convergent adele affine space algebra variety algebraic group automorphism canonical central division algebra central simple algebra character characteristic function classical groups consider convergence factors denote dimension division algebra elements factors for G field finite measure formula Fourier transform function-field G leaving group G group of type Haar measure hardcover hermitian homomorphism idele-module identify induces infinite places integral invariant ISBN isogenous isomorphic Let G mapping Math matrix algebra measure for G modulo morphism multiplicative calculation notations number-field orbit orthogonal group p-adic paperback PM polynomials proof of Lemma proves quadratic extension quadratic form quaternion algebra resp right-hand side semisimple set of convergence shows Siegel's simple algebra special linear group sphere of radius subgroup of G symplectic group Tamagawa measure Tamagawa number torus type L2(b unimodular valuations variety defined vector Witt's theorem write zeta-function