publication . Article . Preprint . 2017

K-groups of reciprocity functors

Ivorra, Florian; Rülling, Kay;
Open Access English
  • Published: 01 Jan 2017
  • Publisher: HAL CCSD
  • Country: France
In this work we introduce reciprocity functors, construct the associated K-group of a family of reciprocity functors, which itself is a reciprocity functor, and compute it in several different cases. It may be seen as a first attempt to get close to the notion of reciprocity sheaves imagined by B. Kahn. Commutative algebraic groups, homotopy invariant Nisnevich sheaves with transfers, cycle modules or K\"ahler differentials are examples of reciprocity functors. As commutative algebraic groups do, reciprocity functors are equipped with symbols and satisfy a reciprocity law for curves.
arXiv: Mathematics::Category TheoryMathematics::K-Theory and HomologyMathematics::Algebraic Topology
free text keywords: [ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG], [ MATH.MATH-KT ] Mathematics [math]/K-Theory and Homology [math.KT], [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], [MATH.MATH-KT]Mathematics [math]/K-Theory and Homology [math.KT], Mathematics - Algebraic Geometry, Mathematics - K-Theory and Homology, Homotopy, Algebraic number, Pure mathematics, Invariant (mathematics), Mathematics, Functor, Reciprocity (social psychology), Reciprocity law, Mathematical analysis, Commutative property
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1.1.5. Lemma. Let X, Y, Z be in Reg61 and [V ] ∈ Cor(X, Y ), [W ] ∈ Cor(Y, Z) be elementary correspondences. Let T be an irreducible component of V ×Y W . Then ˜ W / X 4.2.9. Corollary. Let M1, . . . , Mn−1 be reciprocity functors. Then θX,U (φ ⊗ ψ ⊗ (f × idY ) ◦ h) =

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