2016/03/10 by Gonçalo Tabuada, Tabuada, Goncalo
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #14A22 #14C15 #14F10 #16D30 #18E30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Alkaloids: synthesis and pharmacology #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1603.03411
openalex publication_date 2016/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To every scheme, not necessarily smooth neither proper, we can associate its\ndifferent mixed realizations (de Rham, Betti, etale, Hodge, etc) as well as its\nring of periods. In this note, following an insight of Kontsevich, we prove\nthat, after suitable modifications, these classical constructions can be\nextended from schemes to the broad setting of dg categories. This leads to new\nadditive invariants, which we compute in the case of differential operators, as\nwell as to a theory of periods of dg categories. Among other applications, we\nprove that the ring of periods of a scheme is invariant under projective\nhomological duality. Along the way, we explicitly describe the modified mixed\nrealizations using the Tannakian formalism.\n