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The {\it defect} (also called {\it ramification deficiency}) of valued fieldextensions is a major stumbling block in deep open problems of valuation theoryin positive characteristic. For a detailed analysis, we define and investigatetwo weaker notions of defect: the {\it completion defect} and the {\it defectquotient}. We define them for finite extensions as well as for certain valuedfunction fields (those with "Abhyankar valuations" that are nontrivial on theground field). We investigate both defects and present analogues of the resultsthat hold for the usual defect.

Defects of Algebraic Function Fields, Completion Defects and Defect Quotients