Ivo Dell'Ambrogio

Publications and preprints

In reverse order of writing. The titles mostly link to the corresponding ArXiv page:

28. Stratification in equivariant Kasparov theory
    Joint with Rubén Martos
    Preprint December 2024, 48 pages.
27. A general Greenlees-May splitting principle
    Joint with Serge Bouc and Rubén Martos
    Münster J. Math., to appear. 15 pages.
26. An introduction to Mackey and Green 2-functors
    In Triangulated Categories in Represention Theory and Beyond: The Abel Symposium 2022. Edited by P. A. Bergh, S. Oppermann, and Ø. Solberg. Abel Symposia 17. Springer, Cham (2024), pp 57-84..
25. On Krull-Schmidt bicategories
    Theory Appl. Categ. 38 (2022), no. 8, 232-256.
24. Green 2-functors
    Trans. Amer. Math. Soc. 375 (2022), 7783-7829.
23. Cohomological Mackey 2-functors
    Joint with Paul Balmer
    J. Inst. Math. Jussieu 23 (2024), no. 1, 279-309.
22. The spectrum of equivariant Kasparov theory for cyclic groups of prime order
    Joint with Ralf Meyer
    Ann. K-Theory 6 (2021), no. 3, 543-558.
21. On the comparison of spans and bisets
    Joint with James Huglo
    Cah. Topol. Géom. Différ. Catég. 62 (2021), no. 1, 63-104.
20. Green equivalences in equivariant mathematics
    Joint with Paul Balmer
    Math. Ann. 379 (2021), no. 3, 1315-1342.
19. Axiomatic representation theory of finite groups by way of groupoids
    In Equivariant Topology and Derived Algebra. Edited by S. Balchin, D. Barnes, M. Kedziorek, and M. Szymik. LMS Lecture Notes Series 474. Cambridge University Press (2021), xviii+338.
18. Mackey 2-functors and Mackey 2-motives
    Joint with Paul Balmer
    EMS Monographs in Mathematics. European Mathematical Society, Zürich (2020), viii+227.
17. Mackey algebras which are Gorenstein
    Joint with Jan Šťovíček
    Algebr. Represent. Theor. 23 (2020), 281-284.
16. A note on triangulated monads and categories of module spectra
    Joint with Beren Sanders
    C. R. Math. Acad. Sci. Paris 356 (2018), 839-842.
15. Affine weakly regular tensor triangulated categories (and a small Erratum)
    Joint with Donald Stanley
    Pacific J. Math. 285 (2016), no. 1, 93-109.
14. Gorenstein homological algebra and universal coefficient theorems
    Joint with Greg Stevenson and Jan Šťovíček
    Math. Z. 287 (2017), no. 3, 1109-1155.
13. Grothendieck-Neeman duality and the Wirthmüller isomorphism
    Joint with Paul Balmer and Beren Sanders
    Compositio Math. 152 (2016), 1740-1776.
12. Restriction to finite index subgroups as étale extensions in topology, KK-theory and geometry
    Joint with Paul Balmer and Beren Sanders
    Algebr. Geom. Topol. 15 (2015), no. 5, 3023-3045.
11. An equivariant Lefschetz fixed-point formula for correspondences
    Joint with Ralf Meyer and Heath Emerson
    Documenta Math. 19 (2014) 141-193.
10. A Quillen model for classical Morita theory and a tensor categorification of the Brauer group
    Joint with Gonçalo Tabuada
    J. Pure Appl. Alg. 218 (2014), no. 12, 2337-2355.
9. Even more spectra: tensor triangular comparison maps via graded commutative 2-rings
   Joint with Greg Stevenson
   Appl. Categor. Struct. 22 (2014), no. 1, 169-210.
8. Morita homotopy theory of C*-categories
   Joint with Gonçalo Tabuada
   J. Algebra 398 (2014) 162-199.
7. On the derived category of a graded commutative noetherian ring
   Joint with Greg Stevenson
   J. Algebra 373 (2013) 356-376.
6. Equivariant Kasparov theory of finite groups via Mackey functors
   J. Noncommut. Geom. 8 (2014), no. 3, 837-871.
5. Tensor triangular geometry of noncommutative motives
   Joint with Gonçalo Tabuada
   Adv. Math. 229 (2012), no. 2, 1329-1357.
4. The unitary symmetric monoidal model category of small C*-categories
   Homology, Homotopy Appl. 14 (2012), no. 2, 101-127.
3. Localizing subcategories in the Bootstrap category of separable C*-algebras
   J. K-Theory, 8 (2011), no. 3, 493-505.
2. Tensor triangular geometry and KK-theory
   J. Homotopy Relat. Struct. 5 (2010), no. 1, 319-358.
1. The Witt groups of the spheres away from two
   Joint with Jean Fasel
   J. Pure Appl. Alg. 212 (2008), no. 5, 1039-1045.

Memoirs

• Triangulated categories and applications
  Habilitation memoir (2016), University of Lille 1, 83 pages.
• Prime tensor ideals in some triangulated categories of C*-algebras
  PhD thesis (2008), ETH Zürich, 164 pages. The main results can be found in the article 2. above.
• The Spanier-Whitehead category is always triangulated
  Diploma thesis (2004), ETH Zürich, 39 pages.

Talk slides

• Equivariant homological algebra in tensor-triangulated categories (2025)
• Tensor triangular geometry for equivariant KK-theory (2025)
• Les 2-foncteurs de Mackey et de Green (2024)
  Un exposé de survol donné au CIRM lors de la rencontre annuelle du réseau thématique Algèbre.
• Les 2-foncteurs de Mackey (2023)
  A survey talk given in French at the Caen algebra and geometry seminar.
• A survey of Mackey and Green 2-functors (2023)
  A survey talk given at CIRM at the ANR ChroK closure conference to an audience of topologists (video).
• On Krull-Schmidt bicategories (2022)
  A talk given online at the Malga seminar (Padova + Verona), presenting some ideas from the article nr. 25 above.
• On the origins of classical Green functors (2022)
  Some ideas from the article nr. 24 above, as presented to a Mackey-friendly audience in Amiens.
• Green 2-functors (2022)
  The same ideas from the article nr. 24 above, as presented to a triangulated audience in Aalesund.
• Spans, bisets and blocks (2021)
  Presentation of the results of article nr. 23 above, at The work of Serge Bouc conference.
• A categorification of Yoshida's theorem for Mackey functors (2021)
  Presentation of the results of article nr. 23 above, given at CRM Barcelona (video).
• An introduction to Mackey 2-functors (2021)
  A talk introducing Mackey 2-functors to category theorists, given at ItaCa Fest 2021 (video).
• La correspondance de Green dans les mathématiques équivariantes (2021)
  Un exposé sur quelques résultats de l'article nr. 20 ci-haut.
• The spectrum of equivariant Kasparov theory for cyclic groups of prime order (2020)
  Presentation of the results of article nr. 22 above.
• The Green correspondence in algebraic geometry (2020)
  Presentation of some results from article nr. 20.
• Un regard sur l'infini mathématique (2016)
  Un exposé introductif sur la théorie des ensemble pour les étudiants du cours Euler à l'EPFL.
  L'exposé était accompagné de cette feuille d'exercices.
• An equivariant Lefschetz formula for smooth actions of compact groups (2014)
  Presentation of some results from article nr. 11.
• Dualités entre l'algèbre et la géométrie (2012)
  Un exposé grand public (mathématique) pour la Journée 2012 du Laboratoire Painlevé.

Other mathematical texts

• Serre duality and geometric morphisms (2019), 4 pages.
  This unpublished note smoothes some wrinkles left unironed in article nr. 13 above.
• Categories and C*-algebras: A commented (very partial) bibliography (2012), 4 pages.
  Once upon a time, I was asked about the use of category theory in connection with C*-algebras, and this was my answer.
• A functorial equivariant K-theory spectrum and an equivariant Lefschetz formula, with H. Emerson, T. Kandelaki and R. Meyer (2011), 20 pages.
  This work is an old preprint which has been superseded by item 11 above and thus will not be submitted for publication. Still, it is occasionally cited for the construction of the functorial equivariant K-heory spectrum for C*-algebras, which didn't make it into the published article.
• Categories of C*-algebras (2009), 9 pages.
  A pedantic write-up of the category theory needed to express Gelfand duality precisely.
• A survey of tensor triangular geometry and applications (2009), 6 pages.
  Extended abstract of lectures given in Oberwolfach on Paul Balmer's tensor triangular geometry.
• Biproducts in triangulated categories (2009), 2 pages.
  Once upon a time I wrote up the exercise that the existence of direct sums follows from the other axioms of a triangulated category.