## Algebraic K-theory and Algebraic Number Theory: Proceedings of a Seminar Held January 12-16, 1987, with Support from the National Science Foundation and Japan Society for the Promotion of ScienceThis volume contains the proceedings of a seminar on Algebraic $K$-theory and Algebraic Number Theory, held at the East-West Center in Honolulu in January 1987. The seminar, which hosted nearly 40 experts from the U.S. and Japan, was motivated by the wide range of connections between the two topics, as exemplified in the work of Merkurjev, Suslin, Beilinson, Bloch, Ramakrishnan, Kato, Saito, Lichtenbaum, Thomason, and Ihara. As is evident from the diversity of topics represented in these proceedings, the seminar provided an opportunity for mathematicians from both areas to initiate further interactions between these two areas. |

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### Contents

1 | |

Cycles and biextensions | 19 |

On the Ktheory of fields | 31 |

The homotopical foundations of algebraic Ktheory | 57 |

Universal HasseWitt classes | 83 |

Swan conductors for characters of degree one in the imperfect residue field case | 101 |

Special values of Selberg zeta functions | 133 |

Groups related to scissorscongruence groups | 151 |

Algebraic Ktheory étale cohomology and torsion algebraic cycles | 311 |

On the homotopy fiber of the map BQA BQA | 343 |

Connexions et classes caractéristiques de Beilinson | 349 |

A note in Ktheory of some Calgebras | 377 |

A finiteness condition equivalent to the Tate conjecture over Fq | 385 |

Survey of algebraic vs étale topological Ktheory | 393 |

Noncommutative number theory | 445 |

Normal subgroups of classical groups over rings and gauge groups | 451 |

Abelian ladic representations associated with Selberg integrals | 159 |

Regulators algebraic cycles and values of Lfunctions | 183 |

Homotopy algebraic Ktheory | 461 |

### Other editions - View all

Algebraic K-theory and Algebraic Number Theory: Proceedings of a Seminar ... Michael R. Stein,R. Keith Dennis No preview available - 1989 |

### Common terms and phrases

abelian group abelian varieties adic algebraic cycles algebraic K-theory algebraically closed field arithmetic assume Beilinson bisimplicial Bloch Chern classes Chow group codimension coefficients complex COROLLARY defined definition Deligne denote différentiable dimension divisor element elliptic curves étale cohomology exact sequence extension factors fibration field F finite field follows formula functor geometric Grothendieck Hence Hodge homology homomorphism homotopy cartesian homotopy equivalence ideal induces injective integer isomorphism K-groups KH(A KH(X Ko(X L-functions Lemma Let F Lichtenbaum Mathematics modular modulo morphisme Notes in Math number field p-adic preprint prime proof PROPOSITION proved quadratic Quillen rational equivalence resp result roots of unity schéma simplicial scheme Selberg sheaf sheaves simplicial set Soulé Spec(A spectral sequence Springer Lecture Notes subgroup surfaces surjective Suslin Tate conjecture theorem topological torsion torsor trivial vector bundle vector bundle torsor weak equivalence zero zeta functions