Algebraic K-theory of the fraction field of topological K-theory

Details Algebraic K-theory of the fraction field of topological K-theory Algebraic K-theory of the fraction field of topological K-theory

2009-11-25

arxiv.org/abs/0911.4781v1

Mathematics

K-Theory and Homology

Scientific paper

We compute the algebraic K-theory modulo p and v_1 of the S-algebra ell/p = k(1), using topological cyclic homology. We use this to compute the homotopy cofiber of a transfer map K(L/p) --> K(L_p), which we interpret as the algebraic K-theory of the "fraction field" of the p-complete Adams summand of topological K-theory. The results suggest that there is an arithmetic duality theorem for this fraction field, much like Tate--Poitou duality for p-adic fields.

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