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Maximal separable intermediate fields of large codegree

Maximal separable intermediate fields of large codegree

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k"> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding="application/x-tex">k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a function field in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n left-parenthesis n greater-than 0 right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">n(n &gt; 0)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> variables over <inline-formula content-type="math/mathml"> …