Absolutely lq-Finite Extensions

Abstract

We describe the lower quasi-finite extensions \(K/k\) of characteristic \(p>0\), which are defined as follows: for every \(n\in \mathbb N, k^{p^{-n}} \cap K/k \) is finite. We are especially interested in examining the absolute case. In this regard, we give necessary and sufficient condition for an absolutely lq-finite extension to be of finite size. Moreover, we show that any extension that is at the same time modular and lq-finite is of finite size. Furthermore, we construct an example of extension \(K/k\) of infinite size such that for any intermediate field L of \(K/k, L\) is of finite size over k.

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Correspondence to El Hassane Fliouet.

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Fliouet, E.H. Absolutely lq-Finite Extensions. Acta Math Vietnam 44, 751–779 (2019). https://doi.org/10.1007/s40306-018-0271-2

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Keywords

  • Purely inseparable
  • Irrationality degree
  • Modular extension
  • q-finite extension
  • lq-finite extension
  • Absolutely lq-finite extension

Mathematics Subject Classification (2010)

  • 12F15