Year: 2023
Type: preprint
Abstract: In this article, we prove the $t$-exactness of a Brylinski-Radon transformation taking values in sheaves on flag varieties. This implies several weak Lefschetz type results for cohomology. In particular, we obtain de Cataldo-Migliorini's P=Dec(F) and Beilinson's basic lemma, the latter was an important ingredient in their proof of P=Dec(F). Our methods also allow the sharpening of Esnault-Katz's cohomological divisibility theorem and estimates for the Hodge level. Finally, we upgrade P=Dec(F) to an equivalence of functors which is also valid over a base.
Source: arXiv (Cornell University)
Authors: Rai, Ankit, Shuddhodan, K. V.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4387076111