Bousfield Classes and Ohkawa's Theorem Nagoya, Japan, August 28-30, 2015
-
- Hardcover
- Taschenbuch ausgewählt
- eBook
-
Sprache:Englisch
145,99 €
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Taschenbuch
Erscheinungsdatum
19.03.2021
Abbildungen
X, 435 p.
Herausgeber
Takeo Ohsawa + weitereVerlag
Springer SingaporeSeitenzahl
435
Maße (L/B/H)
23,5/15,5/2,3 cm
Gewicht
769 g
Auflage
1st ed. 2020
Sprache
Englisch
ISBN
978-981-15-1590-3
This volume originated in the workshop held at Nagoya University, August 28–30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the stable homotopy category
SH
form a set. An inspiring, extensive mathematical story can be narrated starting with Ohkawa's theorem, evolving naturally with a chain of motivational questions:
Ohkawa's theorem states that the Bousfield classes of the stable homotopy category
SH
surprisingly forms a set, which is still very mysterious. Are there any toy models where analogous Bousfield classes form a set with a clear meaning?
The fundamental theorem of Hopkins, Neeman, Thomason, and others states that the analogue of the Bousfield classes in the derived category of quasi-coherent sheaves
D
qc
(
X
) form a set with a clear algebro-geometric description. However, Hopkins was actually motivated not by Ohkawa's theorem but by his own theorem with Smithin the triangulated subcategory
SH
c
, consisting of compact objects in
SH
. Now the following questions naturally occur: (1) Having theorems of Ohkawa and Hopkins-Smith in
SH
, are there analogues for the Morel-Voevodsky A
1
-stable homotopy category
SH
(
k
), which subsumes
SH
when
k
is a subfield of
C
?, (2) Was it not natural for Hopkins to have considered
D
qc
(
X
)
c
instead of
D
qc
(
X
)? However, whereas there is a conceptually simple algebro-geometrical interpretation
D
qc
(
X
)
c
=
D
perf
(
X
), it is its close relative
D
b
coh
(
X
) that traditionally, ever since Oka and Cartan, has been intensively studied because of its rich geometric and physical information.
This book contains developments for the rest of the storyand much more, including the chromatics homotopy theory, which the Hopkins–Smith theorem is based upon, and applications of Lurie's higher algebra, all by distinguished contributors.
Noch keine Bewertungen vorhanden
Verfassen Sie die erste Bewertung zu diesem Artikel
Helfen Sie anderen Kundinnen und Kunden durch Ihre Meinung.
Kurze Frage zu unserer Seite
Vielen Dank für Ihr Feedback
Wir nutzen Ihr Feedback, um unsere Produktseiten zu verbessern. Bitte haben Sie Verständnis, dass wir Ihnen keine Rückmeldung geben können. Falls Sie Kontakt mit uns aufnehmen möchten, können Sie sich aber gerne an unseren Kund*innenservice wenden.
zum Kundenservice