I’ve posted a new paper on the arXiv. Most of the results premiered at Oberwolfach, but since then I’ve added an interesting new example inspired by related work of Takehiko Yasuda, whom I met there. (Oberwolfach at work!)
The paper shows that the Kodaira vanishing theorem can fail on smooth Fano varieties of any characteristic p > 0. Taking cones over some of these varieties, we give the first examples of terminal singularities which are not Cohen-Macaulay. By a different method, we construct a terminal singularity of dimension 3 (the lowest possible) in characteristic 2 which is not Cohen-Macaulay.
Image: Palmerston, Foreign Office cat, sneaks up on cheese; from his DiploMog twitter feed