Wednesday 11 February 2026 at 4:45 pm, as part of the Insalate di Matematica seminar cycle, Carolyn Echter (University of Regensburg) will give the following talk
Title: Abstract weight filtrations
Abstract: Weight filtrations have their origin in "Théorie de Hodge: II, III" (1971, 74): While classical Hodge theory yields pure Hodge structures on the cohomology groups of smooth projective complex varieties, Deligne extends this by constructing a filtration on the cohomology of an arbitrary complex variety such that the graded pieces are pure. He refers to the resulting filtered objects as mixed Hodge structures. Mixed structures later appeared also in other contexts, such as the theory of Galois representations, and they share many features, for example they form abelian categories. Weights are closely related to slopes: Both control when nonzero morphisms are admissible. The key difference is that slope filtrations and weight filtrations are indexed in the opposite sense. Based on André's formalisation of slope filtrations, we will set up an abstract framework within which the shared properties of mixed structures become a formal consequence of this fact.
Keywords: Weight and slope filtrations, Mixed Hodge structures
Information to attend
The seminar will be held in Room U9-09 (U9 Building | Viale dell’Innovazione 10, Milano) and will also be available online by this link (password: insalate, 46725283 from phones).
For more information, visit the website