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- W84380989 abstract "AbstractWe now begin the development of cohomology in number theory. As a ground field we take a nonarchimedean local field k, i.e. a field which is complete with respect to a discrete valuation and has a finite residue field. This covers two cases, namely p-adic local fields, i.e. finite extensions of (mathbb{Q}_{p}) for some prime number p, and fields of formal Laurent series (mathbb{F}((t))) in one variable over a finite field. For the basic properties of local fields we refer to [160], chapters II and V. As always, (bar{k}|k) denotes a separable closure of k and K|k the subextensions of (bar{k}|k). v k denotes the valuation of k, normalized by (v_{k}(k^{times}) = mathbb{Z}), and κ the residue field. For every Galois extension K|k we set $$H^i(K|k) := H^i(G(K|k),K^{times}),quad i geq 0. $$ If K|k is finite, we also set (hat{H}^{i}(K|k) = hat{H}^{i}(G(K|k),K^{times})) for (i in mathbb{Z}). The basis for the results in this chapter is the following theorem.Mathematics Subject Classification11Gxx11Rxx11Sxx12Gxx14Hxx20Jxx" @default.
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- W84380989 date "2008-01-01" @default.
- W84380989 modified "2023-09-23" @default.
- W84380989 title "Cohomology of Local Fields" @default.
- W84380989 doi "https://doi.org/10.1007/978-3-540-37889-1_7" @default.
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