Standard Conjecture D for matrix factorizations

2019/05/12 by Brown, Michael K., Walker, Mark E.
#14A22 #14B05 #18E30 #32S25 #32S35 #32S55 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1905.04626

Abstract

We prove the non-commutative analogue of Grothendieck's Standard Conjecture D for the dg-category of matrix factorizations of an isolated hypersurface singularity in characteristic 0. Along the way, we show the Euler pairing for such dg-categories of matrix factorizations is positive semi-definite.

Related

• Standard conjecture D for local stacky matrix factorizations
• Classifying dg-categories of matrix factorizations
• Matrix factorizations and singularity categories for stacks
• Thom-Sebastiani & Duality for Matrix Factorizations
• Matrix factorizations with more than two factors