On groups interpretable in various valued fields

• Yatir Halevi ^[1] ; Assaf Hasson ^[2] ; Ya acov Peterzil ^[1]
  1. [1] University of Haifa

     University of Haifa

     Israel

     
  2. [2] Department of Mathematics, Ben Gurion University of the Negev, Israel
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 4, 2024, págs. 1-64
• Idioma: inglés
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• Resumen

  • We study infinite groups interpretable in three families of valued fields: V-minimal, power bounded T -convex, and p-adically closed fields. We show that every such group G has unbounded exponent and that if G is dp-minimal then it is abelian-byfinite. Along the way, we associate with any infinite interpretable group an infinite type-definable subgroup which is definably isomorphic to a group in one of four distinguished sorts: the underlying valued field K, its residue field k (when infinite), its value group , or K/O, where O is the valuation ring. Our work uses and extends techniques developed in Halevi et al. (Adv Math 404:108408, 2022) to circumvent elimination of imaginaries.