scholarly journals Witt vectors of non-commutative rings and topological cyclic homology

1997 ◽  
Vol 178 (1) ◽  
pp. 109-141 ◽  
Author(s):  
Lars Hesselholt
Keyword(s):  
Commutative Rings ◽  
Cyclic Homology ◽  
Witt Vectors ◽  
Topological Cyclic Homology

scholarly journals On the algebraic K-theory of truncated polynomial algebras in several variables

2014 ◽  
Vol 13 (1) ◽  
pp. 57-81 ◽  
Author(s):  
Vigleik Angeltveit ◽  
Teena Gerhardt ◽  
Michael A. Hill ◽  
Ayelet Lindenstrauss
Keyword(s):  
Positive Characteristic ◽  
Polynomial Algebra ◽  
Cyclic Homology ◽  
Perfect Field ◽  
Polynomial Algebras ◽  
Trace Map ◽  
Witt Vectors ◽  
Several Variables ◽  
Topological Cyclic Homology ◽  
Field Of Positive Characteristic

AbstractWe consider the algebraic K-theory of a truncated polynomial algebra in several commuting variables, . This naturally leads to a new generalization of the big Witt vectors. If k is a perfect field of positive characteristic we describe the K-theory computation in terms of a cube of these Witt vectors on ℕn. If the characteristic of k does not divide any of the ai we compute the K-groups explicitly. We also compute the K-groups modulo torsion for k = ℤ.To understand this K-theory spectrum we use the cyclotomic trace map to topological cyclic homology, and write as the iterated homotopy cofiber of an n-cube of spectra, each of which is easier to understand.

scholarly journals Homology operations in the topological cyclic homology of a point

2010 ◽  
Vol 14 (2) ◽  
pp. 755-772 ◽  
Author(s):  
Håkon Schad Bergsaker ◽  
John Rognes
Keyword(s):  
Cyclic Homology ◽  
Homology Operations ◽  
Topological Cyclic Homology

scholarly journals Relative K-theory and topological cyclic homology

1997 ◽  
Vol 179 (2) ◽  
pp. 223-242 ◽  
Author(s):  
Bjørn Ian Dundas
Keyword(s):  
Cyclic Homology ◽  
Topological Cyclic Homology ◽  
K Theory
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