Title: A p-adic cohomology version of the canonicity of rational Gorenstein singularities

Abstract: I will present a joint work with Jefferson Baudin, Linus Rösler and Maciej Zdanowicz about a p-adic cohomology version of the birational geometry statement that rational Gorenstein singularities are canonical. Our variant states that normal, Q_p-rational, quasi-Gorenstein, F-pure singularities are canonical in dimension 3 and also in dimension 4 if we assume resolution of singularities and we exclude a few low characteristics. In the proof, the classification of compact closed real 2-manifolds is crucially used, as well as the fact that the real projective plane has 2-torsion singular second cohomology. I will explain the importance and the definition of the notions in the statement, as well as bits of the proof, including how the above topological statements show up.