Title: | Automorphisms and symbols in K(,2) |

Author(s): | Holdener, Judy Ann |

Doctoral Committee Chair(s): | Evans, Graham |

Department / Program: | Mathematics |

Discipline: | Mathematics |

Degree Granting Institution: | University of Illinois at Urbana-Champaign |

Degree: | Ph.D. |

Genre: | Dissertation |

Subject(s): | Mathematics |

Abstract: | Much of the work in algebraic K-theory today is devoted to the search for "motivic cohomology." This hoped-for cohomology theory of algebraic geometry should be analogous to the known singular homology groups of topology. In this work we consider Goodwillie and Lichtenbaum's candidate for motivic cohomology. For R a regular ring, they define a "weight" filtration on the K-theory space K(R),$$K(R) = W\sp0 \gets W\sp1 \gets W\sp2 \gets \cdots,$$and then define the cohomology groups to be$$H\sp{m}(X,\doubz (t)) = \pi\sb{2t-m}(W\sp{t}/W\sp{t+1}).$$If what they propose is correct, then one would expect $\pi\sb{t}(W\sp{t}/W\sp{t+l})$ to be the weight t part of K(R). Here we present Goodwillie's proof that this is indeed the case when t = 2 and R is an algebraically closed field. We then continue his work by showing that $\pi\sb2(W\sp2/W\sp3)$ $\cong$ K$\sb2(R)$ for other fields, namely, we handle the cases, R = $\IR$, and R = $\doubc((T)).$ Our arguments also work when R is a finite field. |

Issue Date: | 1994 |

Type: | Text |

Language: | English |

URI: | http://hdl.handle.net/2142/21180 |

Rights Information: | Copyright 1994 Holdener, Judy Ann |

Date Available in IDEALS: | 2011-05-07 |

Identifier in Online Catalog: | AAI9512397 |

OCLC Identifier: | (UMI)AAI9512397 |