On the motivic Segal conjecture

The Segal Conjecture for Cyclic Groups

where /4(G) denotes the completion of the Burnside ring of G with respect to the ideal of virtual G-sets of degree 0. The conjecture was proved for G = Z/(2) by W. H. Lin [5], [3] and for G = Z/(p), where p is an odd prime, by J. H. C. Gunawardena [4]. In this note we outline a proof for G cyclic. We will assume that G has prime power order as the general case follows easily. The proofs cited a...

The Segal Conjecture for Cyclic Groups and its Consequences

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Motivic Zeta Functions of Abelian Varieties, and the Monodromy Conjecture

We prove for abelian varieties a global form of Denef and Loeser’s motivic monodromy conjecture. More precisely, we prove that for any abelian C((t))-variety A, its motivic zeta function has a unique pole at Chai’s base change conductor c(A) of A, and that the order of this pole equals one plus the potential toric rank of A. Moreover, we show that for any embedding of Ql in C, the value exp(2πi...

Bloch-Kato conjecture and motivic cohomology with finite coefficients

THE SEGAL CONJECTURE FOR ELEMENTARY ABELIAN p-GROUPS-II. p-ADIC COMPLETION IN EQUIVARIANT COHOMOLOGY

This result implies an analogue for general finite groups, but we refer the reader to [25] and especially [S] for that. We shall give as efficient a proof of the theorem as present technology seems to allow, starting from the purely algebraic Ext calculation [4,1.1] of Adams, Gunawardena, and Miller as a given. When G=(Zp)‘, the theorem is due to those authors. However, their original passage f...