Building on results of Bazzoni–Šťovíček, we give an explicit construction of an infinite family of commutative rings which generalise the first counterexample on the generalised telescope conjecture of Bernhard Keller in 1994. In particular, the telescope conjecture for their derived categories does not hold. Generalising the construction of these rings further, we give a complete classification of the frame of smashing ideals for the derived category of a finite dimensional valuation domain. As a consequence, we deduce that the Krull dimension of the Balmer spectrum and the smashing spectrum can differ arbitrarily for rigidly-compactly generated tensor-triangulated categories. The talk is based on joint work with Scott Balchin, see https://arxiv.org/abs/2407.11791.

tba