The Henselian defect for valued function fields

Ohm, Jack

doi:10.1090/S0002-9939-1989-0975654-7

The Henselian defect for valued function fields
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Proc. Amer. Math. Soc. 107 (1989), 299-308 Request permission

Abstract:

The notion of defect for finite algebraic extensions of valued fields is classical and due to Ostrowski. Recently Matignon has generalized Ostrowski’s definition to rk 1 (residually transcendental) valued function fields and used it to prove a very sharp version of the genus reduction inequality for $1 - \dim$ function fields. The further generalization of the notion of defect to valued function fields of arbitrary rk is treated here.

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