As a non-connoisseur of arithmetic and arithmetic geometry, I would like to ask about some terminology, which meaning I haven't been able to find out on some books, nor on wikipedia, nor by google. ...
If $L$ is algebraically closed, fields of transcendence degree one over $L$ correspond to algebraic curves over $L$ up to birational equivalence, and finite extensions correspond to finite Galois ...
It is not uncommon to describe interesting classes of field extensions by declaring that an extension $L|K$ belongs to that class if some type of problem with $K$-coefficiens has a property over $L$ ...
This is a follow-up to the following answer: Solvable class field theory in which it is stated as a "folklore" conjecture that the maximal solvable extension of Q is pseudo algebraically closed ...
Consider the extension Q(a,b) of the field of rationals, where a,b are algebraically independent transcendentals. To Q(a,b) adjoin the roots of the polynomials x^5+a^5=1 and y^5+b^5=1. The resulting ...
Consider the transcendental extension Q(t) of the field of rationals. To Q(t) adjoin the root of the polynomial x^5+t^5=1. The resulting field Q(t)[x] is a radical extension of Q(t). Is it true that ...