Finite cyclic tame extensions of kp((t))

Abstract

Let p be a prime number and let ℚ/ℤ′ be the elements in ℚ/ℤ of order prime to p. Let Δ = ℚ/ℤ′ × 1/c-1 ℤ/ℤ × 1/c-1 ℤ/ℤ, where c is a prime power of p. We use characters and valuation theory to prove that Δ is a parameter space for the cyclic tame extensions of the formal Laurent series field kp((t)) of degree prime to p. Furthermore, we construct the cyclic tame extension corresponding to a given triple in Δ. The structure of finite cyclic tame extensions of the p-adic number fields was thoroughly investigated by A. A. Albert in 1935. Here we get the same result as consequence of our main theorem. © 2008 World Scientific Publishing Company.