Motivic Euler Characteristic of Nearby Cycles and a Generalized Quadratic Conductor Formula

2021/01/07 by Azouri, Ran · 2 citations
#14B05 #14E18 #14F42 (Primary) #19G12 #32S30 #32S55 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2101.02686

Abstract

We compute the motivic Euler characteristic of Ayoub's nearby cycles spectrum in terms of strata of a semi-stable reduction, for a degeneration to multiple semi-quasi-homogeneous singularities. This allows us to compare the local picture at the singularities with the global conductor formula for hypersurfaces developed by Levine, Pepin Lehalleur and Srinivas, revealing that the formula is local in nature, thus extending it to the more general setting considered in this paper. The result is a quadratic refinement to the Milnor number formula with multiple singularities.

Cited by

• Motivic nearby cycles and their monodromy at a singular point
• The Motivic Picard--Lefschetz Formula

Related

• Motivic nearby cycles and their monodromy at a singular point
• The quadratic Artin conductor of a motivic spectrum
• Euler characteristics of homogeneous and weighted-homogeneous hypersurfaces
• The Motivic Picard--Lefschetz Formula
• Motivic Milnor fibers of plane curve singularities