JournalsggdVol. 19, No. 2pp. 495–503

First-order model theory and Kaplansky’s stable finiteness conjecture for surjunctive groups

  • Tullio Ceccherini-Silberstein

    Università del Sannio, Benevento, Italy; Istituto Nazionale di Alta Matematica “Francesco Severi”, Roma, Italy
    ORCID

  • Michel Coornaert

    Université de Strasbourg, France

  • Xuan Kien Phung

    Université de Montréal, Montréal, Québec, Canada
    ORCID
First-order model theory and Kaplansky’s stable finiteness conjecture for surjunctive groups cover
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Abstract

Using algebraic geometry methods, the third author proved that the group ring of a surjunctive group with coefficients in a field is always stably finite. In other words, every group satisfying Gottschalk’s conjecture also satisfies Kaplansky’s stable finiteness conjecture. Here, we present a proof of this result based on the first-order model theory.

Cite this article

Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung, First-order model theory and Kaplansky’s stable finiteness conjecture for surjunctive groups. Groups Geom. Dyn. 19 (2025), no. 2, pp. 495–503

DOI 10.4171/GGD/885