Clik here to view.
Hilbert’s Theorem 90…the math
So now that I’ve presented the origins of Hilbert’s Theorem 90, I thought it might be good to actually present it mathematically with a proof. Statement: Suppose K is a finite Galois extension of F...
View ArticleClik here to view.
Generalized HT90
I officially promise this is my last post on Hilbert’s Theorem 90, but because of that it is going to go really fast for those who have not seen group cohomology (it is really cool, so I couldn’t pass...
View ArticleClik here to view.
Descent Theory
I’m going to do a change in plan. Galois Theory: Let F be a field. In some sense the “universal” Galois group is where is the algebraic closure, since given any algebraic extension we have that . In...
View ArticleClik here to view.
Finite Groups as Galois Groups
So my old proof isn’t really working on wordpress for some reason, so I’ve taken it as a sign to do it in a different way. This method is far more complicated than the old way (in which I just call...
View ArticleClik here to view.
Separable Algebras 3
Fix a field and let be a separable closure. Let . Today we prove the strongest structure theorem so far: The category of separable -algebras is anti-equivalent to the category of finite -sets (where...
View Article
