The Birch and Swinnerton-Dyer Conjecture for Abelian Varieties over Number Fields
نویسنده
چکیده
1 Algebraic Groups 7 1.1 Group Varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Restriction of Scalars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Algebraic Groups over a Nonalgebraically Closed Field K . . . . . . . . . . . 13 1.4 Structure of Algebraic Groups . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Topologizing G(R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5.1 Discrete Valuation Rings . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5.2 Adèlic Points on Varieties . . . . . . . . . . . . . . . . . . . . . . . . 18 1.6 Defining a Measure on G(R) . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.7 Tamagawa Measures on G(AK) . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.7.1 Compatibility with Restriction of Scalars . . . . . . . . . . . . . . . . 26
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