Luc Illusie

Luc Illusie

Professeur retraité
Laboratoire de Mathématique, Bât. 307
Université Paris-Saclay
91405 Orsay Cedex - France

Courrier électronique :
Bureau : 2J3
Téléphone : 33 1 40 44 94 31

Publications depuis 2006

Miscellany on traces in l-adic cohomology : a survey, Japanese Journal of Math. 1-1 (2006), 107-136.https://rdcu.be/beBYL
Erratum to : Miscellany on traces in l-adic cohomology : a survey, Japanese Journal of Math. 2-2 (2007), 313-314. https://rdcu.be/bfKuX
"La descente galoisienne", Moscow Math. Journal 9-1 (2009), 47-55. pdf
A Tribute to Henri Cartan (with P. Cartier and J-P. Serre), Notices of the AMS, 57-8 (2010), 946-975. pdf
Reminiscences of Grothendieck and His School (with A. Beilinson, S. Bloch, V. Drinfeld et al.), Notices of the AMS, 57-9 (2010), 1106-1115. pdf
(with W. Zheng) Odds and ends on finite group actions and traces, arXiv:1001.1982, Int. Math. Res. Not. 2013, 1-62; doi: 10.1093/imrn/rnr226, Errata and Addenda, Int. Math. Res. Not., Advance Access, doi: 10.1093/imrn/rnt009.
Torsten Ekedahl : quelques souvenirs, hommage à Torsten Edekahl, décédé le 23.11.2011, SMS bulletinen, décembre 2011, Gazette des Mathématiciens 132, SMF, avril 2012 pdf
(with C. Nakayama and T. Tsuji) On log flat descent, Proc. Japan Academy 89, Ser. A, 1 (2013), 1-5. pdf
Pierre Deligne et la géométrie arithmétique, Gazette des Mathématiciens 138, 2013, 49-53, Erratum, Gazette des Mathématiciens 139, 2014, p. 49, pdf
(avec Y. Laszlo et F. Orgogozo) Travaux de Gabber sur l'uniformisation locale et la cohomologie étale des schémas quasi-excellents, Séminaire à l'École polytechnique 2006-2008, Astérisque 363-364, 2014, pdf
Grothendieck et la cohomologie étale, in Alexandre Grothendieck: A Mathematical Portrait, L. Schneps, ed., International Press, 2014, 175-192. pdf
Grothendieck at Pisa: crystals and Barsotti-Tate groups, Colloquium de Giorgi 2013 and 2014, U. Zannier, ed., Scuola Normale Superiore di Pisa 2015, 79-107. pdf
Around the Poincaré lemma, after Beilinson, Acta Mathematica Vietnamica 40(2), 2015, 231-253. pdf
Elementary abelian l-groups and mod l equivariant étale cohomology algebras, in De la géométrie algébrique aux formes automorphes (II), Une collection d'articles en l'honneur du soixantième anniversaire de Gérard Laumon, Astérisque 369, 2015, 177-195.pdf
From Pierre Deligne's secret garden: looking back at some of his letters, Japan. J. Math. 10, 237-248 (2015). pdf https://rdcu.be/bViAa
(with Michel Raynaud) Grothendieck and algebraic geometry, Asia Pacific Mathematics Newsletter, Jan. 2015, Vol. 5, No. 1, 1-5, and EMS Newsletter, March 2015, vol. 95, 45-50.
(with W. Zheng) Quotient stacks and equivariant étale cohomology algebras: Quillen's theory revisited, J. Algebraic Geom. (2016), no. 2, 289-400. arXiv:1305.0365
Around the Thom-Sebastiani theorem, with an appendix by Weizhe Zheng, Manuscripta Math., 2016 (), 1-65, DOI 10.1007/s00229-016-0852-0
Grothendieck and vanishing cycles, Ann. Fac. Sci. Toulouse Math. (6) 30 (2021), no. 1, 83-115. https://doi.org/10.5802/afst.1667 pdf
A new approach to de Rham-Witt complexes after Bhatt, Lurie, and Mathew, Rend. Sem. Mat. Univ. Padova 146 (2021), 177-221.pdf
Constructibilité générique et uniformité en l, Tunis. J. Math. 4 (2022), no. 1, 159-181. https://doi.org/10.2140/tunis.2022.4.159 pdf
Grothendieck and differential calculus, Comptes Rendus Mathématique 363 (2025), 829-841. https://doi.org/10.5802/crmath.764 pdf

Divers

Errata Complexe cotangent et déformations I, SLN 239, Springer-Verlag 1971, pdf
Errata Complexe cotangent et déformations II, chap. VIII, SLN 283, Springer-Verlag 1972, pdf
Errata Cotangent complex and deformations of torsors and group schemes, Toposes, algebraic geometry and logic, SLN 274, Springer-Verlag 1972, 159-189, pdf
Errata Complexe de de Rham-Witt et cohomologie cristalline, Ann. scient. ENS, 4ème série, t. 12, 1979, 501-661, pdf
Errata SGA 5 III, pdf
Errata Autour du théorème de monodromie locale, dans Périodes p-adiques, Séminaire de Bures, 1988, Astérisque 223, 1994, 9-57, pdf
Errata Catégories dérivées et dualité, travaux de J.-L. Verdier, L'Enseignement math. 36 (1990), 369-391, pdf
Erratum Sur la formule de Picard-Lefschetz, Algebraic Geometry 2000, Azumino (Hotaka) Adv. Stud. Pure Math., 36, Math. Soc. Japan, Tokyo (2002), 249-268, pdf
Errata Grothendieck's existence theorem in formal geometry, in Fundamental Algebraic Geometry, Grothendieck's FGA Explained, AMS Math. Surveys and Monographs 123, 2005, 181-233, pdf
Errata Frobenius and Hodge degeneration, in Introduction to Hodge Theory, J. Bertin, J.-P. Demailly, L. Illusie, and C. Peters, eds., SMF/AMS Texts and Monographs 8, 2002, 99-149, and Frobenius et dégénérescence de Hodge, in Introduction à la théorie de Hodge, J. Bertin, J.-P. Demailly, L. Illusie, et C. Peters, éds., Panoramas et Synthèses 3, SMF, 1996, 113-168, pdf
Erratum Pierre Deligne et la géométrie arithmétique, Gaz. Math. 138 (2013), 49-53, pdf
Errata Quotient stacks and equivariant étale cohomology algebras: Quillen's theory revisited, J. Algebraic Geometry 25 (2016), 289-400, pdf
Erratum Déformations de groupes de Barsotti-Tate, Séminaire sur les pinceaux arithmétiques : la conjecture de Mordell (L. Szpiro, Ed.), VI, 151-198, Astérisque 127, SMF, 1985, pdf
Vanishing cycles over general bases, after P. Deligne, O. Gabber, G. Laumon and F. Orgogozo, pdf
Logarithmic Kummer étale sites and Hodge degeneration, pdf
Old and new in étale cohomology, Wolfson lectures, Manchester (2006), pdf
Deligne's tubular neighborhoods in étale cohomology, Conference in honor of J. Steenbrink, Nijmegen, May 31 - June 2, 2007, pdf
On Gabber's refined uniformization [Ga1] , Talks at the Univ. Tokyo, Jan. 17, 22, 31, Feb. 7, 2008, pdf
On finite group actions, Deligne-Mumford stacks, and traces, after W. Zheng et al., Conference in honor of T. Katsura, July 6, 2008, Univ. Tokyo, pdf
Review of de Rham-Witt theory, $p$-adic Geometry and Homotopy Theory, Loen (Norway), Aug. 2-8, 2009, pdf
Independence of families of l-adic representations and uniform constructibility (after J-P. Serre), prenotes for talks at the Univ. of Tokyo, 2010, pdf
Vanishing theorems and Shimura varieties, after K.-W. Lan and J. Suh, Workshop on Algebraic Geometry, Fudan Univ., Shanghai, Oct. 8, 2010, pdf
De Rham-Witt complexes and p-adic Hodge theory, Pre-notes for Sapporo seminar, March 2011, pdf, pdf
Interview of Luc Illusie by Ulf Persson, Jan. 17, 2012 pdf
From Pierre Deligne's secret garden: looking back at some of his letters, beamer slides of a talk in NYC for an event organized by Friends of the IHES, Oct. 5, 2013, pdf
Glimpses on vanishing cycles, from Riemann to today, beamer slides of a talk given at the Riemann conference, Sanya, China, Dec. 27, 2015, pdf
p-adic cohomologies: history, and new developments, beamer slides of Landau lectures, Institute of Mathematics, The Hebrew University of Jerusalem, May 16, 20, 21, 2019, pdf
Grothendieck and the six operations, beamer slides of a talk given at The fifth international conference on history of modern mathematics, Xi'an, China, Aug. 18-24, 2019, pdf
Partial degeneration of Hodge to de Rham spectral sequences and Kodaira type vanishing theorems for locally complete intersections in positive characteristic, preprint, 2020, pdf
Revisiting Deligne-Illusie, beamer slides of a talk given at the Conference Arithmetic Geometry -Takeshi60, Sept. 10, 2021, pdf
New perspectives on de Rham cohomology, after Bhatt-Lurie, Drinfeld et al, beamer slides of a talk given at the Conference Periods, Motives and Differential Equations (Yves André60), April 11, 2022, pdf
New advances on de Rham cohomology in positive or mixed characteristic, after Bhatt-Lurie, Drinfeld, and Petrov, beamer slides of a talk given at the Conference Around p-adic cohomologies (Bruno Chiarellotto 60), September 22, 2022, pdf
The Kan lectures. Lectures on the de Rham complex. Utrecht, The Netherlands, Dec. 15, 16, 2022, pdf
Revisiting deformations of Barsotti-Tate groups. Chicago, March 6, 2023, pdf
On the Hodge to de Rham spectral sequence in positive characteristic, after A. Petrov. Princeton, Feb. 14, 2023; Chicago, Feb. 27, 2023. pdf
The posterity of Residues and Duality, 2024. pdf
Chronology and posterity of SGA 5, 2025. pdf

Département de Mathématiques
Université Paris-Sud, Bât. 307
F-91405 Orsay Cedex (France)