54 citations · 182 across the 24 of their papers we have counts for
28 papers
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…
An introduction to Mackey and Green 2-functors
Ivo Dell'Ambrogio
For half a century, Mackey and Green functors have been successfully used to model the induction and restriction maps which are ubiquitous in the representation theory of finite gr…
On Krull-Schmidt bicategories
Ivo Dell'Ambrogio
We study the existence and uniqueness of direct sum decompositions in additive bicategories. We find a simple definition of Krull-Schmidt bicategories, for which we prove the uniqu…
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…
Cohomological Mackey 2-functors
Paul Balmer, Ivo Dell'Ambrogio
We show that the bicategory of finite groupoids and right-free permutation bimodules is a quotient of the bicategory of Mackey 2-motives introduced in arXiv:1808.04902, obtained by…
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.
On the comparison of spans and bisets
Ivo Dell'Ambrogio, James Huglo
We compare the bicategory of spans with that of bisets (a.k.a. bimodules, distributors, profunctors) in the context of finite groupoids. We construct in particular a well-behaved p…
Green equivalences in equivariant mathematics
Paul Balmer, Ivo Dell'Ambrogio
We establish Green equivalences for all Mackey 2-functors, without assuming Krull-Schmidt. By running through the examples of Mackey 2-functors, we recover all variants of the Gree…
Axiomatic representation theory of finite groups by way of groupoids
Ivo Dell'Ambrogio
We survey several notions of Mackey functors and biset functors found in the literature and prove some old and new theorems comparing them. While little here will surprise the expe…
Mackey 2-functors and Mackey 2-motives
Paul Balmer, Ivo Dell'Ambrogio
We study collections of additive categories , indexed by finite groups and related by induction and restriction in a way that categorifies usual Mackey functors…
Mackey algebras which are Gorenstein
Ivo Dell'Ambrogio, Jan Šťovíček
We complete the picture available in the literature by showing that the integral Mackey algebra is Gorenstein if and only if the group order is square-free, in which case it must h…
A note on triangulated monads and categories of module spectra
Ivo Dell'Ambrogio, Beren Sanders
Consider a monad on an idempotent complete triangulated category with the property that its Eilenberg-Moore category of modules inherits a triangulation. We show that any other tri…
Affine weakly regular tensor triangulated categories
Ivo Dell'Ambrogio, Donald Stanley
We prove that the Balmer spectrum of a tensor triangulated category is homeomorphic to the Zariski spectrum of its graded central ring, provided the triangulated category is genera…
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…
Grothendieck-Neeman duality and the Wirthmüller isomorphism
Paul Balmer, Ivo Dell'Ambrogio, Beren Sanders
We clarify the relationship between Grothendieck duality à la Neeman and the Wirthmüller isomorphism à la Fausk-Hu-May. We exhibit an interesting pattern of symmetry in the existen…
Restriction to finite-index subgroups as étale extensions in topology, KK-theory and geometry
Paul Balmer, Ivo Dell'Ambrogio, Beren Sanders
For equivariant stable homotopy theory, equivariant KK-theory and equivariant derived categories, we show how restriction to a subgroup of finite index yields a finite commutative…
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 Quillen model for classical Morita theory and a tensor categorification of the Brauer group
Ivo Dell'Ambrogio, Gonçalo Tabuada
Let K be a commutative ring. In this article we construct a symmetric monoidal Quillen model structure on the category of small K-categories which enhances classical Morita theory.…
Even more spectra: tensor triangular comparison maps via graded commutative 2-rings
Ivo Dell'Ambrogio, Greg Stevenson
We initiate the theory of graded commutative 2-rings, a categorification of graded commutative rings. The goal is to provide a systematic generalization of Paul Balmer's comparison…
Morita homotopy theory of C*-categories
Ivo Dell'Ambrogio, Goncalo Tabuada
In this article we establish the foundations of the Morita homotopy theory of C*-categories. Concretely, we construct a cofibrantly generated simplicial symmetric monoidal Quillen…
On the derived category of a graded commutative noetherian ring
Ivo Dell'Ambrogio, Greg Stevenson
For any graded commutative noetherian ring, where the grading group is abelian and where commutativity is allowed to hold in a quite general sense, we establish an inclusion-preser…
Equivariant Kasparov theory of finite groups via Mackey functors
Ivo Dell'Ambrogio
Let G be a finite group. We systematically exploit general homological methods in order to reduce the computation of G-equivariant KK-theory to topological equivariant K-theory. Th…
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…