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

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Ramified complete discrete valuation rings as extensions

Suppose $O$ is a complete discrete valuation ring with uniformizer $\pi$ and residue field $k=O/\pi O$ of charactersitc $p>0$. If $\nu$ is the $\pi$-adic valuation on $K=Frac(O)$, suppose also that $ …