$P=W$ phenomena in algebraic and enumerative geometry
Camilla Felisetti
TL;DR
This paper reviews recent developments in the P=W conjecture within algebraic geometry, highlighting how P=W phenomena manifest across various areas and providing a detailed sketch of a recent proof.
Contribution
It synthesizes recent results on the P=W conjecture and offers a comprehensive overview of its appearances and proofs in algebraic geometry.
Findings
Recent proofs of P=W conjecture reviewed
P=W phenomena appear in multiple algebraic geometry areas
Sketch of Maulik, Shen, and Yin's proof provided
Abstract
In view of the recent proofs of the P=W conjecture, the present paper reviews and relates the latest results in the field, with a view on how P=W phenomena appear in multiple areas of algebraic geometry. As an application, we give a detailed sketch of the proof of P=W by Maulik, Shen and Yin.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology