Motivic nearby cycles and their monodromy at a singular point

2025/11/10 by Ran Azouri, Azouri, Ran
Mathematics · #Algebraic Geometry and Number Theory #Advanced Combinatorial Mathematics #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/arxiv.2511.07668

Abstract

In this survey, we explain how to compute both the quadratic Euler characteristic of nearby cycles, and the motivic monodromy, at a quasi-homogeneous singularity. This gives, for such singularity, a quadratic refinement to the Deligne--Milnor formula in characteristic zero, and an enhancement of the Picard--Lefschetz formula to Voevodsky motives with rational coefficients.

Citations

• The Motivic Picard--Lefschetz Formula
• Proof of the Deligne-Milnor conjecture
• Symmetric powers of null motivic Euler characteristic
• Motivic monodromy and p-adic cohomology theories
• Motivic Euler Characteristic of Nearby Cycles and a Generalized Quadratic Conductor Formula
• Euler characteristics of homogeneous and weighted-homogeneous hypersurfaces
• A¹-Euler classes: six functors formalisms, dualities, integrality and linear subspaces of complete intersections
• Traces in symmetric monoidal categories

Related

• The Motivic Picard--Lefschetz Formula
• Motivic Euler Characteristic of Nearby Cycles and a Generalized Quadratic Conductor Formula
• Motivic nearby cycles functors, local monodromy and universal local acyclicity
• Log motivic nearby cycles
• Nearby cycles at infinity as a triangulated functor