The tower of  K ‐theory of truncated polynomial algebras | Zendy

Hesselholt Lars | Zendy

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The tower of K ‐theory of truncated polynomial algebras

Author(s) -

Hesselholt Lars

Publication year - 2008

Publication title -

journal of topology

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.447

H-Index - 31

eISSN - 1753-8424

pISSN - 1753-8416

DOI - 10.1112/jtopol/jtm007

Subject(s) - mathematics , tower , noetherian , noetherian ring , prime (order theory) , ring (chemistry) , projection (relational algebra) , group (periodic table) , algebra over a field , combinatorics , polynomial , pure mathematics , discrete mathematics , finitely generated abelian group , mathematical analysis , chemistry , civil engineering , organic chemistry , algorithm , engineering

Let A be a regular noetherian F p ‐algebra. The relative K ‐groups K q ( A [ x ]/( x m ),( x )) and the Nil‐groups Nil q ( A [ x ]/( x m )) were evaluated by the author and Ib Madsen in terms of the big de Rham–Witt groups W r Ω A q of the ring A . In this paper, we evaluate the maps of relative K ‐groups and Nil‐groups induced by the canonical projection f : A [ x ]/( x m ) → A [ x ]/( x n ). The result depends strongly on the prime p . It generalizes earlier work by Stienstra on the groups in degrees 2 and 3.

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