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 τ (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 τ (n) is known only for n 7. In this paper we assume that k is a field of characteristic p > 0 and study the essential dimension of inseparable exte… Show more
“…Surprisingly, the case where e ≠ Ø (i.e., the polynomials f(x) in question are not separable) turns out to be easier. We refer the reader to [53], where an exact formula for ed(n, e) is obtained.…”
Section: Essential Dimension Of a Polynomialmentioning
“…Surprisingly, the case where e ≠ Ø (i.e., the polynomials f(x) in question are not separable) turns out to be easier. We refer the reader to [53], where an exact formula for ed(n, e) is obtained.…”
Section: Essential Dimension Of a Polynomialmentioning
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.