2023/09/25 by Ankit Rai, K. V. Shuddhodan, Rai, Ankit +1
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.2309.13973
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.