Back to Algebraic Geometry Seminar: Fall 2021
Algebraic Geometry Seminar
Date: Tuesday, Nov 30, 2021
Time: 3:30PM - 4:30PM
Location: Zoom
Oishee Banerjee
HCM Bonn
Title |
Filtration of cohomology via symmetric (semi)simplicial spaces |
Abstract |
Inspired by Deligne’s use of the simplicial theory of hypercoverings in defining mixed Hodge structures we replace the indexing category ∆ by the symmetric simplicial category ∆S and study (a class of) ∆S-hypercoverings, which we call spaces admitting symmetric (semi)simplicial filtration . For ∆S-hypercoverings we construct a spectral sequence, somewhat like the Cˇech-to-derived category spectral sequence. The advantage of working on ∆S is that all of the combinatorial complexities that come with working on ∆ are bypassed, giving simpler, unified proof of known results like the computation of (in some cases, stable) singular cohomology (with rational coefficients) and étale cohomology (with Q_l coefficients) of the moduli space of degree (n) maps (C) to a projective space, (C) a smooth projective curve of genus (g), of unordered configuration spaces, that of the moduli space of smooth sections of a fixed (g_d^r) that is (m)-very ample etc. |
Algebraic Geometry