Extension of Fields: Norm and Valuation

Related lectures (32)

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Covers the construction of Qp, norms, valuations, and Ostrovski's theorem.

Explores ramification and structure of finite extensions of Qp, including unramified extensions and Galois properties.

Covers the approximation of functions in Sobolev spaces using smooth functions.

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.

Covers the uniqueness of norm extension in finite fields and the construction of norms on finite extensions of Qp.

Explores real estate investment valuation, construction costs, and property pricing factors.

Covers the algebraic closure of Qp and the definition of p-adic complex numbers, exploring roots' continuous dependence on coefficients.

Explores the definition of Q_p and the completion of Q,1(p) to form Qp.

Covers the properties of finite dimensional algebras and non-semisimple representations.