Some hypersurface singularities over the p-adic integers

par Marta Benozzo

jeudi 16 oct. 2025, 14:00 → 16:00 Europe/Paris

M7-411

Even when trying to classify smooth varieties, it is natural to stumble upon singular varieties. Recently, there has been a lot of progress in the classification of varieties over fields of positive characteristics and over mixed characteristic DVR's like Z_p. This has been possible partly thanks to the introduction of new notions of singularities related to Frobenius splittings and perfectoid methods, respectively.

Given a hypersurface in a projective space over the complex numbers, we can measure how singular it is with an invariant called the ''log canonical threshold''. Similarly, in positive characteristic, we can define the ''F-pure threshold'' and in mixed characteristic the ''plus-pure threshold''. In this talk, we will explore some examples of how to compute the plus-pure threshold and how this relates to the invariants in positive characteristic and in characteristic 0.

This is based on joint work with V. Jagathese, V. Pandey, P. Ramírez-Moreno, K. Schwede, P. Sridhar.