Hilbert's Theorem 90

The mathematical sentence that David Hilbert listing under the number 90 in his theory of algebraic number fields and has since borne that name, makes a statement about the structure of certain field extensions.

Original version

It is a cyclic Galois extension and a producer of the associated Galois group. Then, each with norm of the form

With a suitable.

Galoiskohomologische version

Is a body, a Galois field extension and. Then it follows for the Galoiskohomologie:

Algebraic - geometric version

It is a schema. Then

In other words: Every étale - locally trivial line bundle is already a Zariski - line bundle.

Hilbert 90 for motivic cohomology

The original version of generalized in the motivic cohomology for cyclic Galoisüberlagerungen with producer Sigma. For the spectrum of a body will be returned in the original version.

  • Number Theory
  • Algebraic Geometry
  • Set ( mathematics)
Spectrum of a ring
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