Relations between the Chow motive and the noncommutative motive of a smooth projective variety

2013/03/13 by Marcello Bernardara, Bernardara, Marcello, Gonçalo Tabuada +1 · 2 citations
Mathematics · #11E04 #13D09 #14A22 #14C15 #14K05 #19C30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1303.3172

openalex publication_date 2013/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we relate the notions of Lefschetz type, decomposability, and isomorphism, on Chow motives with the notions of unit type, decomposability, and isomorphism, on noncommutative motives. Examples, counter-examples, and applications are also described.

Cited by

• Weil transfer of noncommutative motives
• Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) noncommutative motives

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