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Corrigendum to "Model Theory of Fields with Virtually Free Group Actions"

Özlem Beyarslan, Piotr Kowalski

Abstract

There is an irreparable error in the proof of Theorem 3.26 in our "Model Theory of Fields with Virtually Free Group Actions" paper and we withdraw the claim of having proved that theorem. In fact, that theorem is false in a very strong sense.

Corrigendum to "Model Theory of Fields with Virtually Free Group Actions"

Abstract

There is an irreparable error in the proof of Theorem 3.26 in our "Model Theory of Fields with Virtually Free Group Actions" paper and we withdraw the claim of having proved that theorem. In fact, that theorem is false in a very strong sense.

Paper Structure

This paper contains 19 sections, 39 theorems, 146 equations.

Table of Contents

  1. Introduction
  2. Transformal kernels and model companions
  3. Functor
  4. Transformal kernels
  5. Transformal kernels and axioms of ACFA
  6. Word Problem Diagonals
  7. Virtually free groups
  8. Finite groups
  9. Amalgamated products
  10. HNN-extensions
  11. General case
  12. Semi-direct products
  13. Model-theoretic properties
  14. General properties
  15. Simplicity and beyond
  16. ...and 4 more sections

Key Result

Lemma 2.2

On the level of coordinate rings, we have the following commutative diagram: \xymatrix{ K[V] \ar[d]^{\sigma_V} & & K[W]\ar[ll]_{\varphi^*} \ar[d]^{\sigma_W} \\ K[{}^{\sigma}V] & & K[{}^{\sigma}W]\ar[ll]_{\left({}^{\sigma}\varphi\right)^*}.}

Theorems & Definitions (100)

  • Remark 2.1
  • Lemma 2.2
  • Lemma 2.3
  • proof
  • Definition 2.4
  • Remark 2.5
  • Proposition 2.6
  • proof
  • Definition 2.7
  • Lemma 2.8
  • ...and 90 more