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2016•Annals of K-TheoryOpen access

The local symbol complex of a reciprocity functor

Evangelia Gazaki

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Abstract

For a reciprocity functor M we consider the local symbol complexwhere C is a smooth complete curve over an algebraically closed field k with generic point η C and ⊗ M is the product of Mackey functors.We prove that if M satisfies certain assumptions, then the homology of this complex is isomorphic to the K-group of reciprocity functors T (M, CH 0 (C) 0 )(Spec k).MSC2010: 14C25.

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For a reciprocity functor M we consider the local symbol complexwhere C is a smooth complete curve over an algebraically closed field k with generic point η C and ⊗ M is the product of Mackey functors.We prove that if M satisfies certain assumptions, then the homology of this complex is isomorphic to the K-group of reciprocity functors T (M, CH 0 (C) 0 )(Spec k).MSC2010: 14C25.

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Available abstract

For a reciprocity functor M we consider the local symbol complexwhere C is a smooth complete curve over an algebraically closed field k with generic point η C and ⊗ M is the product of Mackey functors.We prove that if M satisfies certain assumptions, then the homology of this complex is isomorphic to the K-group of reciprocity functors T (M, CH 0 (C) 0 )(Spec k).MSC2010: 14C25.

Key concepts: Functor, Mathematics, Reciprocity (cultural anthropology), Algebraically closed field, Homology (biology), Combinatorics, Field (mathematics), Product (mathematics)

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