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- W2015291600 abstract "In his doctor thesis (Mem. Acad. Roy. Belg. 11, No. 4 (1937), 1–110), M. Krasner proved the following theorem (in Hilbert's terminology): Let k be a field of algebraic numbers (or P-adic field), K a normal extension of k of finite degree, P a prime ideal of K, e the ramification order of P in Kk, p the characteristic of the residual field (mod P), h the greatest factor of e prime to p, vq the qth ramification number and nq the order of the qth ramification group Vq of Kk. Then, (nq − nq + 1) vq ≡ 0 (mod h). This result is easily extended to the classical case (valuation of k discrete, the residual extension Kk of Kk separable), and is given for this case (with the proof similar to that of Krasner) by J.-P. Serre in “corps locaux” (Herman, Paris, 1968). Here we prove an analoguous, but more complicated result, for arbitrary normal extensions (of finite degree) of discretely valued fields and for some situations in the case of dense valuations." @default.
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- W2015291600 date "1988-01-01" @default.
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- W2015291600 title "A property of ramification groups and numbers of algebraic finite extensions of valued fields" @default.
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- W2015291600 doi "https://doi.org/10.1016/0022-314x(88)90116-3" @default.
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