54 citations · 182 across the 24 of their papers we have counts for
10 papers · 1 filter
Stratification in equivariant Kasparov theory
Ivo Dell'Ambrogio, Rubén Martos
We study stratification, that is the classification of localizing tensor ideal subcategories by geometric means, in the context of Kasparov's equivariant KK-theory of C*-algebras.…
A general Greenlees-May splitting principle
Serge Bouc, Ivo Dell'Ambrogio, Rubén Martos
In equivariant topology, Greenlees and May used Mackey functors to show that, rationally, the stable homotopy category of -spectra over a finite group splits as a product of…
Green 2-functors
Ivo Dell'Ambrogio
We extend the theory of Mackey 2-functors introduced in arXiv:1808.04902 by defining the appropriate notion of rings, namely Green 2-functors. After providing the first results of…
The spectrum of equivariant Kasparov theory for cyclic groups of prime order
Ivo Dell'Ambrogio, Ralf Meyer
We compute the Balmer spectrum of the equivariant bootstrap category of separable -C*-algebras when is a group of prime order.
Gorenstein homological algebra and universal coefficient theorems
Ivo Dell'Ambrogio, Greg Stevenson, Jan Stovicek
We study criteria for a ring - or more generally, for a small category - to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the un…
An equivariant Lefschetz fixed-point formula for correspondences
Ivo Dell'Ambrogio, Heath Emerson, Ralf Meyer
We compute the trace of an endomorphism in equivariant bivariant K-theory for a compact group G in several ways: geometrically using geometric correspondences, algebraically using…
A functorial equivariant K-theory spectrum and an equivariant Lefschetz formula
Ivo Dell'Ambrogio, Heath Emerson, Tamaz Kandelaki +1
We construct a symmetric spectrum representing the G-equivariant K-theory of C*-algebras for a compact group or a proper groupoid G. Our spectrum is functorial for equivariant *-ho…
Tensor triangular geometry of non-commutative motives
Ivo Dell'Ambrogio, Goncalo Tabuada
In this article we initiate the study of the tensor triangular geometry of the categories Mot(k)_a and Mot(k)_l of non-commutative motives (over a base ring k). Since the full comp…
Localizing subcategories in the Bootstrap category of separable C*-algebras
Ivo Dell'Ambrogio
Using the classical universal coefficient theorem of Rosenberg-Schochet, we prove a simple classification of all localizing subcategories of the Bootstrap category of separable com…
Tensor triangular geometry and KK-theory
Ivo Dell'Ambrogio
We present some results on equivariant KK-theory in the context of tensor triangular geometry. More specifically, for G a finite group, we show that the spectrum of the tensor tria…