Finite Tor dimension and failure of coherence in absolute integral closures (Q1376298)

Let \(R\) be a commutative ring with identity. The authors show that if either \(R\) is a perfect ring of characteristic \(p>0\) or else \(R/pR\) is perfect, then under additional conditions, the radical of a finitely generated ideal has finite Tor dimension. As application, it is proved that \(R^+\) is not coherent when \(R\) is a Noetherian domain of dimension \(\geq 3\), and, under additional restrictions, when \(\dim (R)=2\), where \(R^+\) denotes the integral closure of the domain \(R\) in an algebraic closure of its field of fractions.