Vol. 1, No. 3, 2016

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The local symbol complex of a reciprocity functor

Evangelia Gazaki

Vol. 1 (2016), No. 3, 317–338

For a reciprocity functor we consider the local symbol complex

(MG m)(ηC) PC(k) (k),

where C is a smooth complete curve over an algebraically closed field k with generic point ηC and M is the product of Mackey functors. We prove that if satisfies certain assumptions, then the homology of this complex is isomorphic to the K-group of reciprocity functors T(, CH ¯ 0(C)0)(Speck).

reciprocity functor, Milnor $K$-group, local symbol
Mathematical Subject Classification 2010
Primary: 14C25
Received: 26 May 2015
Revised: 21 July 2015
Accepted: 10 August 2015
Published: 18 July 2016
Evangelia Gazaki
Department of Mathematics
University of Chicago
5734 University Avenue
Chicago, IL 60637
United States