A guided tour through the garden of noncommutative motives

Abstract

These are the extended notes of a survey talk on noncommutative motives given at the 3era Escuela de Inverno Luis Santalo - CIMPA Research School: Topics in Noncommutative Geometry, Buenos Aires, July 26 to August 6, 2010.

17 pages

References in corpus (3)

• Motivic structures in non-commutative geometry
• Noncommutative motives, numerical equivalence, and semi-simplicity
• The fundamental theorem via derived Morita invariance, localization, and A^1-homotopy invariance

Cited by in corpus (16)

• On the derived category of the classical Godeaux surface
• Noncommutative motives of Azumaya algebras
• Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields
• Noncommutative Motives I: A Universal Characterization of the Motivic Stable Homotopy Theory of Schemes
• Quantization via Linear homotopy types
• Noncommutative numerical motives, Tannakian structures, and motivic Galois groups
• Non-existence of exceptional collections on twisted flags and categorical representability via noncommutative motives
• Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) noncommutative motives
• Algebraic K-theory, K-regularity, and T-duality of ${\mathcal{O}}_{\infty }$-stable $C^{\ast }$-algebras
• $C^{\ast }$-algebraic drawings of dendroidal sets
• Rational points on symmetric powers and categorical representability
• Noncommutative Artin motives
• Perfect correspondences and Chow motives
• On derived categories and noncommutative motives of varieties
• Analogy between the cyclotomic trace map $K\to TC$ and the Grothendieck trace formula via noncommutative geometry
• Weil transfer of noncommutative motives