Abstract: Let k be a base field, K be a field containing k and L/K be a field extension of degree n. The essential dimension ed(L/K) over k is a numerical invariant measuring "the complexity" of L/K. Of particular interest is $��$(n) = max { ed(L/K) | L/K is a separable extension of degree n}, also known as the essential dimension of the symmetric group $S_n$. The exact value of $��$(n) is known only for n $\leq$ 7. In this paper we assume that k is a field of characteristic p > 0 and study the essential dimension of inseparable extensions L/K...
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