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The compactness locus of a geometric functor and the formal construction of the Adams isomorphism.
- Source :
-
Journal of Topology . Jun2019, Vol. 12 Issue 2, p287-327. 41p. - Publication Year :
- 2019
-
Abstract
- We introduce the compactness locus of a geometric functor between rigidly‐compactly generated tensor‐triangulated categories, and describe it for several examples arising in equivariant homotopy theory and algebraic geometry. It is a subset of the tensor‐triangular spectrum of the target category which, crudely speaking, measures the failure of the functor to satisfy Grothendieck–Neeman duality (or equivalently, to admit a left adjoint). We prove that any geometric functor — even one which does not admit a left adjoint — gives rise to a Wirthmüller isomorphism once one passes to a colocalization of the target category determined by the compactness locus. When applied to the inflation functor in equivariant stable homotopy theory, this produces the Adams isomorphism. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 17538416
- Volume :
- 12
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Topology
- Publication Type :
- Academic Journal
- Accession number :
- 134826595
- Full Text :
- https://doi.org/10.1112/topo.12089