Titlebook: Basic Number Theory; André Weil Book 19671st edition Springer-Verlag Berlin Heidelberg 1967 Cantor.Mathematica.field.number theory

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Decongestant

The theorem of Riemann-Roch algebraic geometry; this lies outside the scope of this book. The results to be given here should be regarded chiefly as an illustration for the methods developed above and as an introduction to a more general theory.

反话

Simple algebrasthe same properties. Tensor-products will be understood to be taken over the groundfield; thus we write .⊗. instead of .⊗. when . are algebras over ., and .⊗. or .., instead of .⊗., when . is an algebra over . and . a field containing .. being always considered as an algebra over ..

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Simple algebras over local fieldser words, if . is such a homomorphism, and . ∈ ., we write . for the image of . under .. We consider Hom(., .), in an obvious manner, as a vector-space over .; as such, it has a finite dimension, since it is a subspace of the space of .-linear mappings of . into .. As usual, we write End(.) for Hom(.).

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https://doi.org/10.1007/978-1-4613-1507-0ts, and |π.|. = ... If . is of characteristic .>1, we will denote by . the number of elements of the field of constants of . and identify that field with .; then, according to the definitions in Chap. VI, we have .. = .. for every place ..