Algebraic K-Theory and Algebraic Topology by Robert Boltje, G.-Martin Cram, V. P. Snaith (auth.), P. G.

By Robert Boltje, G.-Martin Cram, V. P. Snaith (auth.), P. G. Goerss, J. F. Jardine (eds.)

A NATO complicated research Institute entitled "Algebraic K-theory and Algebraic Topology" used to be held at Chateau Lake Louise, Lake Louise, Alberta, Canada from December 12 to December sixteen of 1991. This publication is the quantity of complaints for this assembly. The papers that seem listed below are consultant of lots of the lectures that got on the convention, and for this reason current a "snapshot" of the country ofthe K-theoretic artwork on the finish of 1991. The underlying aim of the assembly used to be to debate contemporary paintings relating to the Lichtenbaum-Quillen advanced of conjectures, fro~ either the algebraic and topological issues of view. The papers during this quantity care for a number of subject matters, together with motivic cohomology theories, cyclic homology, intersection homology, better classification box idea, and the previous telescope conjecture. This assembly was once together funded through gives you from NATO and the nationwide technology Foun­ dation within the usa. i need to take this chance to thank those organizations for his or her aid. i'd additionally prefer to thank the opposite participants of the organizing com­ mittee, particularly Paul Goerss, Bruno Kahn and Chuck Weibel, for his or her help make the convention winning. This was once the second one NATO complex learn Institute to be held during this venue; the 1st used to be in 1987. The luck of either meetings owes a lot to the professionalism and helpfulness of the management and employees of castle Lake Louise.

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9 sw(x;) = r, fori = 0, ... ,p- 1, sw(xp) = pr- 1. Now choose a non trivial character iJ; of U; = Gal(E/L;), fori= O, ... ,p. 2, but with the number V£p(7rr) = pr. For i = 0, ... ,p- 1, E/ L; is purely ramified, and the conductor of iJ; is given by Axiom 2. ,r. 10 sw(iJ;) = pr-1, fori=O, ... ,p-1, sw(iJp) = pr. 2. 2, we get: p(p- 1)r = 0. = (p- 1) · (p- 1)(pr- 1) + (p- 1)pr. This is a contradiction! References (1] R. Boltje : Canonical and explicit Brauer induction in the character ring of a finite group and a generalisation for Mackey functors; Augsburg Univ.

In the case of a Galois extension of degree p, the classical definition reduces to: 0';( 1rE) sw(1J;) = v E ( - - - 1). 1rE Here 7rE denotes any prime element of E and VE the value of E. 5 sw(1J;) = s, fori=O, ... ,p-1, sw(1Jp) = (t-s)p+s. 32 Now choose a non trivial character Xi of GfU; = Gal(L;/ F), fori= 0, ... ,p. To compute the conductor of the x;, I use the inductivity property and the following induction formula, involving the regular character PU; (resp. Pa;u;) of U; (resp. 6 I: ind8/Pui - P · 1ui) j=O,j¢'i The character PG/U; consists of the trivial character and of p- 1 Galois twists of Xi· The same argument applies to pui" Note that the trivial character has conductor zero (by Axiom · 2).

1. - Related results have been proved by W. Raskind ([R]). 2 above, his paper and the above discussion establish a link between the conjecture that Hd-l(X,Kd) is a torsion group and Bloch's conjecture that V(X'1) is a torsion group. At least when X is a surface, I wonder whether the maximal divisible subgroup of V(X'1) can contain torsion elements. 4. 1). Then the cokernel of the map V(X'1)tors --7 E9 Ao(Xp) PEC(l) is finite, and the group G = Ker[V(X7)) --7 E9 A 0 (Xp )] PEC(l) is torsion-by-divisible.

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