Humboldt University Berlin, Winter 2026/27
Time: Tuesdays 13:15 - 14:45
Venue: Room 3.007, Rudower Chaussee 25, 12489 Berlin
— See also the Algebraic Geometry Seminars at HU and FU —
| 20.10.2026 | Giuseppe Ancona (Strasbourg) |
| Title: | Ramified periods and field of definition |
| Abstract: | In a joint work with Dragos Fratila and Alberto Vezzani, we construct hyperelliptic curves of large genus, defined over quadratic fields that are isomorphic to their Galois conjugates but do not descend to Q. The obstruction to descent is new and we call it "ramified periods". These are p-adic numbers that arise from the comparison between de Rham cohomology and crystalline cohomology (hence the term periods). These numbers can reveal interesting information if p ramifies in the quadratic field. |
| 28.10.2026, 13:15, 3.007, & 29.10.2026, 15:15, 3.008 | Olivier de Gaay Fortman (Imperial College) |
| Title: | p-Adic obstructions to the integral Hodge conjecture |
| Abstract: | In these two talks I will report on a joint (ongoing) project with Emiliano Ambrosi. In the first talk, I will give an overview of the theory of prismatic cohomology, as developed by Bhatt and Scholze. I will also formulate our main result, which links de Rham cohomology of varieties in positive characteristic to integral algebraic cycles on complex varieties. In the second talk, I will prove our main result, which proves non-algebraicity of some integral Hodge classes on various classes of complex algebraic varieties. The technique is to use prismatic cohomology and a suitable specialization to positive characteristic, which « degenerates the cohomology » while keeping the variety smooth. All this is joint work with Emiliano Ambrosi. |
| 3.11.2026, 13:15, 3.007, & 4.11.2026, 15:15, 1.115 | Charles Vial (Bielefeld) |
| Title: | The fundamental group scheme of globally F-regular varieties |
| Abstract: | By theorems of Takayama, Xu and Braun, complex projective log Fano varieties are simply connected, and the fundamental group of their regular locus is finite. In positive characteristic, globally F-regular varieties play the role of log Fano varieties, and torsors under finite group schemes replace étale covers. Krah and I showed that the Nori fundamental group scheme of a globally F-regular projective variety is trivial. I will give a proof of this result, and then explain why the Nori fundamental group scheme of the regular locus is finite and linearly reductive. |
| 10.11.2026 | Gregorio Baldi (Jussieau) |
| Title: | tba |
| Abstract: | tba |
| 24.11.2026 | Javier Fresán (Jussieau) |
| Title: | tba |
| Abstract: | tba |