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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

1 vote
4 answers
730 views

k-th powers in the field of p-adics

In "On definable susbsets of p-adic fields", Macintyre 1976, he states the following fact that, let $x\in Q_p^*$ such that $v(x) = 0$ (where $v$ is the p-adic valuation) and $k\in N$ then there exists …
Silvain Rideau's user avatar
2 votes
3 answers
2k views

Algebraic extensions of p-adic closed fields

I have been working with p-adically closed fields and there are two results that are used time and times again in what I am reading, but I cannot find any references where they are proved... The firs …
Silvain Rideau's user avatar