- The former is related to the Galois cohomology groups of F.
- It can also be defined in terms of Galois cohomology.
- The Galois cohomology of this group scheme is a way of expressing Kummer theory.
- Over a field, the extensions are parametrized by elements of the corresponding Galois cohomology group.
- The study of the Galois cohomology of idele class groups is a central matter in class field theory.
- It's difficult to find galois cohomology in a sentence. 用galois cohomology造句挺難的
- In turn, this led to the notion of Galois cohomology and 閠ale cohomology ( which builds on it ).
- Galois cohomology makes no assumption that Galois groups are abelian groups, so that this was a non-abelian theory.
- These isomorphism classes form the non-abelian Galois cohomology set H ^ 1 ( F, G _ 2 ).
- The earliest results identifiable as Galois cohomology had been known long before, in algebraic number theory and the arithmetic of elliptic curves.
- It leads at once to questions of Galois cohomology, since the torsors represent classes in group cohomology " H " 1.
- The needs of number theory were in particular expressed by the requirement to have control of a local-global principle for Galois cohomology.
- Through an isomorphism, it can be associated with a symbol ( a, P ) in the second Galois cohomology of the field k.
- This may now be explained quickly by Galois cohomology ( which however postdates the introduction of the term by more direct use of Clifford algebras ).
- This can be proved using additive counterparts of the methods involved in Kummer theory, such as Hilbert's theorem 90 and additive Galois cohomology.
- Firstly, Galois cohomology appeared as the foundational layer of 閠ale cohomology theory ( roughly speaking, the theory as it applies to zero-dimensional schemes ).