Fundamental isomorphism conjecture via non‐commutative motives | Zendy

Balmer Paul | Zendy; Tabuada Gonçalo | Zendy

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Fundamental isomorphism conjecture via non‐commutative motives

Author(s) -

Balmer Paul,

Tabuada Gonçalo

Publication year - 2013

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201200057

Subject(s) - mathematics , conjecture , isomorphism (crystallography) , pure mathematics , homology (biology) , invariant (physics) , commutative property , invariant theory , discrete mathematics , algebra over a field , biochemistry , chemistry , crystal structure , mathematical physics , gene , crystallography

Given a group, we construct a “fundamental localizing invariant” on its orbit category. We prove that any isomorphism conjecture valid for this fundamental invariant implies the same isomorphism conjecture for all localizing invariants, like non‐connective K ‐theory, Hochschild homology, cyclic homology, and so on. Then, we discuss how to reduce such a fundamental isomorphism conjecture to essentially K ‐theoretic ones. Finally, we develop the analogue additive results.

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