The K–theory presheaf of spectra

John F. Jardine

Type: Article

Publication Date: 2009-06-16

Citations: 7

DOI: https://doi.org/10.2140/gtm.2009.16.151

Abstract

Some applications are displayed: these include a Galois cohomological descent spectral sequence for the etale K–theory of a scheme (where the Galois group is the Grothendieck fundamental group), and the Morel–Voevodsky description of Thomason–Trobaugh K–theory as Nisnevich K–theory in nonnegative degrees. The is also a spectrum-level description of Voevodsky’s periodicity operator for Nisnevich K–theory.

Locations

CiteSeer X (The Pennsylvania State University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	On Voevodsky's Algebraic K-Theory Spectrum	2009	Ivan Panin K. I. Pimenov Oliver Röndigs
+ PDF Chat	Picard groups of higher real -theory spectra at height	2017	Drew Heard Akhil Mathew Vesna Stojanoska
+ PDF Chat	The Higher K-Theory of Complex Varieties	2000	Claudio Pedrini Charles A. Weibel
+ PDF Chat	ON THE MOTIVIC SPECTRAL SEQUENCE	2015	Grigory Garkusha Ivan Panin
+	The K-Theory Spectrum of Varieties	2015	Jonathan A. Campbell
+	The K-Theory Spectrum of Varieties	2015	Jonathan A. Campbell
+	The Completely Decomposed Topology on Schemes and Associated Descent Spectral Sequences in Algebraic K-Theory	1989	Ye. A. Nisnevich
+	ON ALGEBRAIC K-THEORY SPECTRA	1999	Paul Arne Østvær
+	The homotopy theory of H∞ ring spectra	1986	Robert Bruner
+ PDF Chat	The $K$-theory spectrum of varieties	2018	Jonathan A. Campbell
+	Spectral theory and sheaf theory. II	1986	Mihai Putinar
+	The K-Book: An Introduction to Algebraic K-theory	2013	Charles A. Weibel
+	H∞ ring spectra via space-level homotopy theory	1986	James E. McClure
+	Twisted K-theory in motivic homotopy theory.	2021	Elden Elmanto Denis Nardin Maria Yakerson
+	Topological K-Theory of Algebraic K-Theory Spectra	2000	Stephen Α. Mitchell
+	Lectures in spectral theory	1963	Lucien Waelbroeck
+	A Postnikov Tower for Algebraic K-Theory	1999	Daniel Dugger
+	Spectra in Khovanov and Knot Floer Theories	2024	Sucharit Sarkar Marco Marengon András I. Stipsicz
+	Hodge theory and spectral sequences	1994	Robin Forman
+	ell-adic topological Jacquet-Langlands duality	2023	Andrew Salch Matthias Strauch

Works That Cite This (7)

Action	Title	Year	Authors
+ PDF Chat	The slice spectral sequence for singular schemes and applications	2018	Amalendu Krishna Pablo Pelaez
+ PDF Chat	Existence and uniqueness of $$E_{\infty }$$ E ∞ structures on motivic $$K$$ K -theory spectra	2013	Niko Naumann Markus Spitzweck Paul Arne Østvær
+ PDF Chat	The Motivic Hopf Map Solves the Homotopy Limit Problem for $K$-Theory	2018	Oliver Röndigs Markus Spitzweck Paul Arne Østvær
+	The Local Structure of Algebraic K-Theory	2012	Bjørn Ian Dundas Thomas G. Goodwillie Randy McCarthy
+ PDF Chat	Semitopologization in motivic homotopy theory and applications	2015	Amalendu Krishna Jinhyun Park
+	The Riemann–Roch theorem without denominators in motivic homotopy theory	2013	Satoshi Kondo Seidai Yasuda
+	The Comparison of K-Theory and TC	2012	Bjørn Ian Dundas Thomas G. Goodwillie Randy McCarthy

Works Cited by This (32)

Action	Title	Year	Authors
+ PDF Chat	Simplicial Homotopy Theory	2009	Paul G. Goerss John F. Jardine
+	Bloch-Kato Conjecture and Motivic Cohomology with Finite Coefficients	2000	Andrei Suslin Vladimir Voevodsky
+	Generalized Etale Cohomology Theories	1997	John F. Jardine
+	Higher Algebraic K-Theory	2006	Aderemi O. Kuku
+	On the K-theory of local fields	1984	Andrei Suslin
+ PDF Chat	Presheaves of symmetric spectra	2000	John F. Jardine
+ PDF Chat	The spectral sequence relating algebraic K-theory to motivic cohomology	2002	Eric M. Friedlander
+	Higher algebraic K-theory: I	1973	Daniel Quillen
+ PDF Chat	The Bloch-Kato conjecture and a theorem of Suslin-Voevodsky	2001	Thomas Geisser Marc Levine
+	A homotopy theory for stacks	2008	Sharon Hollander