Seminar / expository notes
Notes
Expository reports prepared for seminars and talks.
Serre Duality for Cohen–Macaulay Schemes and Local Complete Intersections
Seminar on Cohomology of Sheaves and Schemes, SoSe 2026.
A derived treatment of Serre duality for projective Cohen–Macaulay schemes, including the construction and concentration of the dualizing complex, the canonical pairing, the local complete intersection adjunction formula, and the smooth case.
Currents, Residues, and the Bochner–Martinelli Kernel
Oberseminar report, June 2026.
Notes on currents as an enlargement of differential forms, residue identities, the real spherical and Bochner–Martinelli kernels, the blow-up interpretation of the kernel, local Dolbeault homotopy, and the computation of Dolbeault and de Rham cohomology by currents.
Beilinson–Lichtenbaum over Dedekind Domains
Talk report, 23 June 2026.
An exposition of the passage from syntomic Beilinson–Lichtenbaum cohomology to motivic spectra, base change over mixed-characteristic Dedekind domains, the identification of the completed zero slice, and the resulting Beilinson–Lichtenbaum comparison on smooth schemes.