Work

Semistable Lefschetz pencils

Year: 2025

Type: article

Abstract: We study the geometry and cohomology of Lefschetz pencils for semistable schemes over a discrete valuation ring. We relate the global cohomological properties of the Lefschetz pencil and the monodromy-weight conjecture; in particular, we show that if one assumes the monodromy-weight conjecture in smaller dimensions, then one can obtain a rather complete understanding of the relative cohomology of the pencil. This reduces the monodromy-weight conjecture to an arithmetic variant of a conjecture of Kashiwara for the projective line.

Source: Journal für die reine und angewandte Mathematik (Crelles Journal)

DOI: 10.1515/crelle-2025-0084

Authors: Hélène Esnault, Moritz Kerz

Institutions: Freie Universität Berlin, University of Regensburg

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,712

Funder: Deutsche Forschungsgemeinschaft