Caterina (Katia) Consani

Publications and Preprints

  1. On the absolute geometry of \(\operatorname{Spec}\mathbf Z\) (with A. Connes), Preprint 2026.
  2. On the Jacobian of \(\operatorname{Spec}\mathbf Z\) (with A. Connes), to appear in Journal of Noncommutative Geometry, 2026.
  3. Zeta Spectral Triples (with A. Connes and H. Moscovici), to appear in Proceedings of the CIRM conference, Applications of NonCommutative Geometry to Gauge Theories, Field Theories, and Quantum Space-Time, 7-11 April 2025. EMS Press (2026).
  4. Knots, primes and class field theory (with A. Connes), in Regulators V, Contemporary Math. 842 (2026).
  5. On q-series and the moment problem associated to local factors (with A. Connes and H. Moscovici), Preprint 2024.
  6. Knots, primes and the adele class space (with A. Connes). Preprint 2024.
  7. Zeta zeros and prolate wave operators: semilocal adelic operators (with A. Connes and H. Moscovici), Ann. Funct. Anal. 15 (2024), no. 4, Paper No. 87, 38 pp. 2025-Best Paper in Annals of Functional Analysis, Award Winner.
  8. On the metaphysics of \(\mathbf F_1\) (with A. Connes), Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 35 (2024), 121-154
  9. Riemann-Roch for the ring \(\mathbf Z\) (with A. Connes), C. R. Math. Acad. Sci. Paris 362 (2024), 229–235.
  10. BC-system, absolute cyclotomy and the quantized calculus (with A. Connes), to appear in Enseign. Math. (2024). Special volume for Sullivan’s 80-th Birthday.
  11. Riemann-Roch for \(\operatorname{Spec}\mathbf Z\) (with A. Connes), Bulletin des Sciences Mathematiques 187 (2023).
  12. Cyclic theory and the pericyclic category (with A. Connes), in Cyclic Cohomology at 40: Achievements and Future Prospects , 103–122, Proc. Sympos. Pure Math., 105, Amer. Math. Soc., Providence, RI, 2023.
  13. Hochschild homology, trace map and \(\zeta\)-cycles (with A. Connes), in Cyclic Cohomology at 40: Achievements and Future Prospects , 83–101, Proc. Sympos. Pure Math., 105, Amer. Math. Soc., Providence, RI, 2023.
  14. Spectral triples and \(\zeta\)-cycles (with A. Connes), Enseign. Math. 69 (2023), no. 1–2, 93–148. Special volume dedicated to Vaughan Jones.
  15. Quasi-inner functions and local factors (with A. Connes), J. Number Theory 226 (2021) 139–167.
  16. Weil positivity and Trace formula: the archimedean place (with A. Connes), Selecta Mathematica (N.S.) 27, 4, (2021), pp. 1–70.
  17. Segal’s Gamma rings and universal arithmetic (with A. Connes), The Quarterly Journal of Mathematics, 72, 1-2, (2021), pp. 1–29.
  18. The Scaling Hamiltonian (with A. Connes), J. Operator Theory 85 1 (2021), pp. 257– 276.
  19. On Absolute Algebraic Geometry the affine case (with A. Connes), Advances in Mathematics 390 Paper No. 107909 (2021), 44 pp.
  20. \(\operatorname{Spec}\mathbf Z\) and the Gromov norm (with A. Connes), Theory and Applications of Categories, 35, No. 6, (2020), pp. 155–178.
  21. The Riemann-Roch strategy, Complex lift of the Scaling Site (with A. Connes), in “Advances in Noncommutative Geometry, On the Occasion of Alain Connes’ 70th Birthday”, Chamseddine, A., Consani, C., Higson, N., Khalkhali, M., Moscovici, H., Yu, G. (Eds.), Springer (2019).
  22. Homological Algebra in Characteristic One (with A. Connes), Higher Structures Journal 3 (2019), no. 1, 155–247.
  23. Geometry of the Scaling Site (with A. Connes), Selecta Math. (N.S.) 23 (2017), no. 3, 1803–1850.
  24. The Scaling Site (with A. Connes), C. R. Math. Acad. Sci. Paris 354 (2016), no. 1, 1–6.
  25. Absolute Algebra and Segal’s \(\Gamma\)-Rings: au Dessou de \(\operatorname{Spec}\mathbf Z\) (with A. Connes), J. Number Theory 162 (2016), 518–551.
  26. Geometry of the Arithmetic Site (with A. Connes), Adv. Math. 291 (2016), 274–329.
  27. The Cyclic and Epicyclic Sites (with A. Connes), Rend. Semin. Mat. Univ. Padova 134 (2015), 197–237.
  28. Projective Geometry in Characteristic One and the Epicyclic Category (with A. Connes), Nagoya Math. J. 217 (2015), 95–132.
  29. Cyclic Structures and the Topos of Simplicial Sets (with A. Connes), J. Pure Appl. Algebra 219 (2015), no. 4, 1211–1235.
  30. The Universal Thickening of the Field of Real Numbers (with A. Connes), Advances in the theory of numbers, 11–74, Fields Inst. Commun., 77, Fields Inst. Res. Math. Sci., Toronto, ON, 2015.
  31. The Arithmetic Site (with A. Connes), C. R. Math. Acad. Sci. Paris 352 (2014), no. 12, 971–975.
  32. Cyclic Homology, Serre’s Local Factors and the \(\lambda\)-Operations (with A. Connes), J. K- Theory 14 (2014), no. 1, 1–45.
  33. On the Arithmetic of the BC-System (with A. Connes), J. Noncommutative Geometry 8 (2014), no. 3, 873–945.
  34. Noncommutative Geometry, Arithmetic, and Related Topics (Editor with A. Connes), Proceedings of the Twenty-First Meeting of the Japan-U.S. Mathematics Institute, Johns Hopkins University Press (2012).
  35. Characteristic One, Entropy and the Absolute Point (with A. Connes), in Noncommutative geometry, arithmetic, and related topics, 75–139, Johns Hopkins Univ. Press, Baltimore, MD, 2011.
  36. The Hyperring of Ad` ele Classes(with A. Connes), J. Number Theory 131 (2011), no. 2, 159–194.
  37. On the Notion of Geometry over \(\mathbf F_1\) (with A. Connes), J. Algebraic Geometry 20 (2011), no. 3, 525–557.
  38. Schemes over \(\mathbf F_1\) and Zeta Functions (with A. Connes), Compositio Math. 146 (2010), no. 6, 1383–1415.
  39. From Monoids to Hyperstructures: in Search of an Absolute Arithmetic(with A. Connes), in Casimir force, Casimir operators and the Riemann hypothesis, 147–198, Walter de Gruyter, Berlin, 2010.
  40. The Weil Proof and the Geometry of the Adele Class Space (with A. Connes and M. Marcolli), in Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. I, 339–405, Progr. Math., 269, Birkhauser Boston, Inc., Boston, MA, 2009.
  41. Fun with \(\mathbf F_1\) (with A. Connes and M. Marcolli), J. Number Theory 129 (2009), no. 6, 1532–1561. Selected by Elsevier B.V. as Article of the Future 2011 in Mathematics & Computer Science.
  42. Noncommutative Geometry and Motives (a quoi Servent les Endomotifs?), in Renormalization and Galois theories, 1–37, IRMA Lect. Math. Theor. Phys., 15, Eur. Math. Soc., Zurich, 2009.
  43. Noncommutative Geometry and Motives: the Thermodynamics of Endomotives (with A. Connes and M. Marcolli), Adv. Math. 214 (2007), no. 2, 761–831.
  44. Quantum Statistical Mechanics over Function Fields (with M. Marcolli), J. Number Theory 123 (2007), no. 2, 487–528.
  45. Archimedean Cohomology Revisited (with M. Marcolli), in Noncommutative geometry and number theory, 109–140, Aspects Math., E37, Friedr. Vieweg, Wiesbaden, 2006.
  46. Noncommutative Geometry and Number Theory: Where Arithmetic Meets Geometry and Physics (Editor with M. Marcolli), Aspects of Mathematics E37 Vieweg (2006).
  47. On the Cusp Form Motives in Genus One and Level One (with C. Faber), in Moduli spaces and arithmetic geometry, 297–314, Adv. Stud. Pure Math., 45, Math. Soc. Japan, Tokyo, (2006).
  48. Non-commutative Geometry, Dynamics and \(\infty\)-adic Arakelov Geometry (with M. Marcolli), Selecta Math. (N.S.) 10 (2004), no. 2, 167–251.
  49. New Perspectives in Arakelov Geometry (with M. Marcolli), in Number theory, 81–102, CRM Proc. Lecture Notes, 36, Amer. Math. Soc., Providence, RI, 2004. Electronic.
  50. Spectral triples from Mumford Curves (with M. Marcolli), Int. Math. Res. Not. 2003, no. 36, 1945–1972.
  51. Triplets Spectraux en Geometrie d’Arakelov (with M. Marcolli), C. R. Math. Acad. Sci. Paris 335 (2002), no. 10, 779–784.
  52. The Picard-Lefschetz Formula and a Conjecture of Kato: the Case of Lefschetz Fibra- tions (with M. Kim), Math. Res. Lett. 9 (2002), no. 5–6, 621–631.
  53. Arithmetic on a Quintic Threefold (with J. Scholten), Internat. J. Math. 12 (2001), no. 8, 943–972.
  54. The Local Monodromy as a Generalized Algebraic Correspondence (with an appendix by S. Bloch) Doc. Math. 4 (1999), 65–108.
  55. Double Complexes and Euler L–Factors , Compositio Math. 111 (1998), no. 3, 323–358.
  56. Double Complexes and Euler L–Factors on Degenerations of Algebraic Varieties, Thesis (Ph.D.) The University of Chicago. 1996. 63 pp.
  57. K–Theory of Blow–ups and Vector Bundles on the Cone over a Surface, K-Theory 7 (1993), no. 3, 269–284.
  58. Intersection Theories and K-Theory on Singular Varieties (in italian), Ph.D Thesis at The University Turin (and Genoa) (1993).
  59. A Moving–Lemma for a Singular Variety and Applications to the Grothendieck Group \(K_0(X)\), in Algebraic K-theory, Commutative algebra, and Algebraic geometry (Santa Margherita Ligure, 1989), Contemp. Math., 126, Amer. Math. Soc., Providence, RI, (1992), 21–45.