Title :

Grothendieck–Neeman duality and the Wirthmüller isomorphism

Author(s) :

Balmer, Paul [Auteur]
Department of Mathematics [UCLA]
Dell’Ambrogio, Ivo [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Université de Lille
Sanders, Beren [Auteur]

Journal title :

Compositio Mathematica

Pages :

1740-1776

Publisher :

Foundation Compositio Mathematica

Publication date :

2016-05-23

ISSN :

0010-437X

HAL domain(s) :

Mathématiques [math]/Catégories et ensembles [math.CT]
Mathématiques [math]/Géométrie algébrique [math.AG]
Mathématiques [math]/Topologie algébrique [math.AT]
Mathématiques [math]/K-théorie et homologie [math.KT]
Mathématiques [math]/Théorie des représentations [math.RT]

English abstract : [en]

We clarify the relationship between Grothendieck duality à la Neeman and the Wirthmüller isomorphism à la Fausk–Hu–May. We exhibit an interesting pattern of symmetry in the existence of adjoint functors between compactly ...
Show more >We clarify the relationship between Grothendieck duality à la Neeman and the Wirthmüller isomorphism à la Fausk–Hu–May. We exhibit an interesting pattern of symmetry in the existence of adjoint functors between compactly generated tensor-triangulated categories, which leads to a surprising trichotomy: there exist either exactly three adjoints, exactly five, or infinitely many. We highlight the importance of so-called relative dualizing objects and explain how they give rise to dualities on canonical subcategories. This yields a duality theory rich enough to capture the main features of Grothendieck duality in algebraic geometry, of generalized Pontryagin–Matlis duality à la Dwyer–Greenless–Iyengar in the theory of ring spectra, and of Brown–Comenetz duality à la Neeman in stable homotopy theory.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Homotopie chromatique et K-théorie

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T14:12:46Z