The categorified Grothendieck-Riemann-Roch theorem

Autor: Pavel Safronov, Nicolò Sibilla, Marc Hoyois, Sarah Scherotzke
Přispěvatelé: University of Zurich
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Pure mathematics
Categorification
Algebraic geometry
Algebraic topology
01 natural sciences
Mathematics::Algebraic Topology
K-theory
High Energy Physics::Theory
Mathematics - Algebraic Geometry
510 Mathematics
Mathematics::Algebraic Geometry
Mathematics::K-Theory and Homology
Mathematics::Category Theory
0103 physical sciences
FOS: Mathematics
Algebraic Topology (math.AT)
Category Theory (math.CT)
Mathematics - Algebraic Topology
0101 mathematics
Category theory
QA
Algebraic Geometry (math.AG)
19D55 K-theory and homology
cyclic homology and cohomology
Mathematics
Algebra and Number Theory
010102 general mathematics
Grothendieck–Riemann–Roch theorem
K-Theory and Homology (math.KT)
Mathematics - Category Theory
Chern character
10123 Institute of Mathematics
Character (mathematics)
categorification
Mathematics - K-Theory and Homology
010307 mathematical physics
Realization (systems)
14F08 Derived categories of sheaves
dg categories
and related constructions in algebraic geometry
2602 Algebra and Number Theory
Zdroj: Hoyois, M, Safronov, P, Scherotzke, S & Sibilla, N 2021, ' The categorified Grothendieck-Riemann-Roch theorem ', Compositio Mathematica, vol. 157, no. 1, pp. 154-214 . https://doi.org/10.1112/S0010437X20007642
Compositio Mathematica
ISSN: 0010-437X
DOI: 10.1112/S0010437X20007642
Popis: In this paper we prove a categorification of the Grothendieck-Riemann-Roch theorem. Our result implies in particular a Grothendieck-Riemann-Roch theorem for To\"en and Vezzosi's secondary Chern character. As a main application, we establish a comparison between the To\"en-Vezzosi Chern character and the classical Chern character, and show that the categorified Chern character recovers the classical de Rham realization.
Comment: 50 pages. v3: final version
Databáze: OpenAIRE
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