Given a field $K$ of characteristic $p$, a classical result of Jacobson provides a Galois correspondence between finite purely inseparable subfields of exponent one (those with $K^p\subset L\subset K$), and sub-restricted Lie algebras of $\mathrm{Der}(K)$. I will discuss joint work with Lukas Brantner in which we extend this Galois correspondence to subfields of arbitrary exponent using methods from derived algebraic geometry. Speaker(s): Joe Waldron (MSU)
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