de Rham–Witt reading list

S. Bloch, Algebraic K-Theory and Crystalline Cohomology, Publ. Math. IHÉS 47, 187–268. [Numdam]

L. Illusie, Complexe de de Rham–Witt, Astérisque 63, 83–112. [Numdam]

L. Illusie, Complexe de de Rham–Witt et cohomologie cristalline, Ann. Sci. Éc. Norm. Supér. (4) 12, 501–661. [Numdam] [errata]

M. Raynaud, p-Torsion du schéma de Picard, Astérisque 64, 87–148. [Numdam]

N. O. Nygaard, Higher de Rham–Witt Complexes of Supersingular K3 Surfaces, Compositio Math. 42, 245–271. [Numdam]

N. O. Nygaard, Slopes of Powers of Frobenius on Crystalline Cohomology, Ann. Sci. Éc. Norm. Supér. (4) 14, 369–401. [DOI]

L. Illusie, Finiteness, Duality, and Künneth Theorems in the Cohomology of the de Rham–Witt Complex, Lecture Notes in Math. 1016, 20–72. [DOI]

L. Illusie and M. Raynaud, Les suites spectrales associées au complexe de de Rham–Witt, Publ. Math. IHÉS 57, 73–212. [Numdam]

T. Ekedahl, On the Multiplicative Properties of the de Rham–Witt Complex. I, Ark. Mat. 22, 185–239. [DOI]

T. Zink, Cartier Theory of Commutative Formal Groups, Teubner-Texte zur Mathematik 68. [English translation]

R. Crew, On Torsion in the Slope Spectral Sequence, Compositio Math. 56, 79–86. [Numdam]

T. Ekedahl, On the Multiplicative Properties of the de Rham–Witt Complex. II, Ark. Mat. 23, 53–102. [DOI]

M. Gros, Classes de Chern et classes de cycles en cohomologie de Hodge–Witt logarithmique, Mém. Soc. Math. France (N.S.) 21, 1–87. [DOI]

S. Bloch and K. Kato, p-Adic Étale Cohomology, Publ. Math. IHÉS 63, 107–152. [Numdam]

T. Ekedahl, Diagonal Complexes and F-Gauge Structures, Travaux en Cours 18, Hermann, 120 pp.. [record]

J. S. Milne, Values of Zeta Functions of Varieties over Finite Fields, Amer. J. Math. 108, 297–360. [PDF] [addendum]

J.-Y. Étesse, Complexe de de Rham–Witt à coefficients dans un cristal, Compositio Math. 66, 57–120. [Numdam]

L. Illusie, Ordinarité des intersections complètes générales, The Grothendieck Festschrift II, Progr. Math. 87, 376–405.

O. Hyodo, On the de Rham–Witt Complex Attached to a Semi-Stable Family, Compositio Math. 78, 241–260. [Numdam]

A. Mokrane, La suite spectrale des poids en cohomologie de Hyodo–Kato, Duke Math. J. 72, 301–337. [DOI]

O. Hyodo and K. Kato, Semi-Stable Reduction and Crystalline Cohomology with Logarithmic Poles, Astérisque 223, 221–268. [Numdam]

L. Illusie, Réduction semi-stable ordinaire, cohomologie étale p-adique et cohomologie de de Rham, Astérisque 223, 209–220. [Numdam]

L. Hesselholt, On the p-Typical Curves in Quillen’s K-Theory, Acta Math. 177, 1–53. [DOI]

T. Geisser and L. Hesselholt, Topological Cyclic Homology of Schemes, Proc. Sympos. Pure Math. 67, 41–87. [author page]

L. Hesselholt and I. Madsen, On the K-Theory of Local Fields, Ann. of Math. (2) 158, 1–113. [DOI]

S. Bloch, Crystals and de Rham–Witt Connections, J. Inst. Math. Jussieu 3, 315–326. [DOI]

L. Hesselholt and I. Madsen, On the de Rham–Witt Complex in Mixed Characteristic, Ann. Sci. Éc. Norm. Supér. (4) 37, 1–43. [DOI]

K. Joshi, A p-Adic Proof of Hodge Symmetry for Threefolds, C. R. Acad. Sci. Paris, Ser. I 338, 781–786. [DOI] [arXiv]

A. Langer and T. Zink, De Rham–Witt Cohomology for a Proper and Smooth Morphism, J. Inst. Math. Jussieu 3, 231–314. [PDF]

L. Hesselholt, The Absolute and Relative de Rham–Witt Complexes, Compositio Math. 141, 1109–1127. [DOI]

A. Langer and T. Zink, Gauss–Manin Connection via Witt-Differentials, Nagoya Math. J. 179, 1–16. [DOI]

J. S. Milne and N. Ramachandran, The de Rham–Witt and Zₚ-Cohomologies of an Algebraic Variety, Adv. Math. 198, 36–42. [arXiv]

N. Ramachandran, Values of Zeta Functions at s = 1/2, Int. Math. Res. Not. 2005, 1519–1541. [arXiv]

T. Geisser and L. Hesselholt, The de Rham–Witt Complex and p-Adic Vanishing Cycles, J. Amer. Math. Soc. 19, 1–36. [DOI]

P. Berthelot, S. Bloch, and H. Esnault, On Witt Vector Cohomology for Singular Varieties, Compositio Math. 143, 363–392. [DOI]

L. Illusie, Review of de Rham–Witt Theory, Loen lecture notes, 77 pp.. [PDF]

C. Davis, A. Langer, and T. Zink, Overconvergent de Rham–Witt Cohomology, Ann. Sci. Éc. Norm. Supér. (4) 44, 197–262. [DOI]

L. Illusie, De Rham–Witt Complexes and p-Adic Hodge Theory, Sapporo seminar pre-notes. [notes] [log / Hyodo–Kato]

J. S. Milne and N. Ramachandran, The p-Cohomology of Algebraic Varieties and Special Values of Zeta Functions, J. Inst. Math. Jussieu 14, 801–835. [arXiv]

B. Bhatt, M. Morrow, and P. Scholze, Integral p-Adic Hodge Theory, Publ. Math. IHÉS 128, 219–397. [arXiv]

L. Hesselholt, Topological Hochschild Homology and the Hasse–Weil Zeta Function, Contemp. Math. 708, 157–180. [arXiv]

T. Nikolaus and P. Scholze, On Topological Cyclic Homology, Acta Math. 221, 203–409. [DOI]

B. Bhatt, M. Morrow, and P. Scholze, Topological Hochschild Homology and Integral p-Adic Hodge Theory, Publ. Math. IHÉS 129, 199–310. [arXiv]

L. Illusie, p-Adic Cohomologies: History, and New Developments, Landau lecture slides. [PDF]

L. Illusie, Partial Degeneration of Hodge to de Rham Spectral Sequences and Kodaira Type Vanishing Theorems for Locally Complete Intersections in Positive Characteristic, preprint. [PDF]

K. Joshi, Crystalline Aspects of Geography of Low Dimensional Varieties I: Numerology, European J. Math. 6, 1111–1175. [DOI] [arXiv]

S. Molokov, Prismatic Cohomology and de Rham–Witt Forms, arXiv:2008.04956v3; to appear in Sbornik: Mathematics. [arXiv]

B. Antieau and T. Nikolaus, Cartier Modules and Cyclotomic Spectra, J. Amer. Math. Soc. 34, 1–78. [DOI]

B. Bhatt, J. Lurie, and A. Mathew, Revisiting the de Rham–Witt Complex, Astérisque 424, viii+158 pp.. [arXiv]

L. Illusie, A New Approach to de Rham–Witt Complexes, after Bhatt, Lurie, and Mathew, Rend. Sem. Mat. Univ. Padova 146, 177–221. [PDF]

S. Mondal, Dieudonné Theory via Cohomology of Classifying Stacks, Forum Math. Sigma 9, e81. [arXiv]

B. Antieau and D. Bragg, Derived Invariants from Topological Hochschild Homology, Algebraic Geometry 9, 364–399. [arXiv]

B. Bhatt and J. Lurie, Absolute Prismatic Cohomology, preprint, 242 pp.. [arXiv]

B. Bhatt and J. Lurie, The Prismatization of p-Adic Formal Schemes, preliminary version. [arXiv]

L. Illusie, Lectures on the de Rham Complex, Daniel Kan Lectures. [PDF]

L. Illusie, New Advances on de Rham Cohomology in Positive or Mixed Characteristic, after Bhatt–Lurie, Drinfeld, and Petrov, lecture slides. [PDF]

L. Illusie, New Perspectives on de Rham Cohomology, after Bhatt–Lurie, Drinfeld, et al., lecture slides. [PDF]

A. Mathew, Some Recent Advances in Topological Hochschild Homology, Bull. Lond. Math. Soc. 54, 1–44. [arXiv]

S. Mondal, A Computation of Prismatic Dieudonné Module, Acta Arith. 205, 87–96. [PDF]

S. Mondal, Gₐᵖᵉʳᶠ-Modules and de Rham Cohomology, Adv. Math. 409, 108691. [arXiv]

S. Mondal, Reconstruction of the Stacky Approach to de Rham Cohomology, Math. Z. 302, 687–693. [arXiv]

Y. Nakkajima, Artin–Mazur Heights and Yobuko Heights of Proper Log Smooth Schemes of Cartier Type, and Hodge–Witt Decompositions and Chow Groups of Quasi-F-Split Threefolds, J. Reine Angew. Math. 787, 1–44. [arXiv]

B. Bhatt, Prismatic F-Gauges, Princeton Math 549 lecture notes. [course] [PDF]

F. Yobuko, Quasi-F-Split and Hodge–Witt, arXiv:2312.00682v1. [arXiv]

F. Andriopoulos, TR and the r-Nygaard Filtered Prismatic Cohomology, arXiv:2412.00914v2. [arXiv]

F. Andriopoulos, TR with Logarithmic Poles and the de Rham–Witt Complex, arXiv:2412.00929v1. [arXiv]

K. Bals, The Topological Cartier–Raynaud Ring, arXiv:2404.10724v1. [arXiv]

V. Drinfeld, Prismatization, Selecta Math. (N.S.) 30, Paper 49. [arXiv]

R. Fernando, Saturated de Rham–Witt Complexes with Unit-Root Coefficients, arXiv:2406.02922v2. [arXiv]

K. Magidson, Witt Vectors and δ-Cartier Rings, arXiv:2409.03877v4. [arXiv]

Z. Mao, Noncommutative Relative de Rham–Witt Complex via the Norm, arXiv:2410.05998v1. [arXiv]

J. McCandless, On Curves in K-Theory and TR, J. Eur. Math. Soc. 26, 4315–4373. [arXiv]

M. Darrell and N. Riggenbach, TR of Quasiregular Semiperfect Rings Is Even, Selecta Math. (N.S.) 31, Article 63. [arXiv]

S. K. Devalapurkar and S. Mondal, p-Typical Curves on p-Adic Tate Twists and de Rham–Witt Forms, Adv. Math. 479, 110448. [arXiv]

E. Dotto, An Analogue of the Milnor Conjecture for the de Rham–Witt Complex in Characteristic 2, Forum Math. Sigma 13, e87. [arXiv]

E. Dotto, A. Krause, T. Nikolaus, and I. Patchkoria, Witt Vectors with Coefficients and TR, Proc. Lond. Math. Soc. (3) 130, e70047. [arXiv]

R. Fernando, Dimensional Vanishing of the Saturated de Rham–Witt Complex, arXiv:2507.22314v2. [arXiv]

L. Grammatica, A. N. Skorobogatov, and Y. Yang, Brauer Groups of Abelian Varieties over Fields of Finite Characteristic, arXiv:2511.08840v2. [arXiv]

S. Mondal, T. Moulinos, and L. Yang, Artin–Mazur Formal Groups and Milne Duality via Unipotent Spectra, arXiv:2510.06152v1. [arXiv] [PDF]

S. Mondal, Dieudonné Theory via Classifying Stacks and Prismatic F-Gauges, arXiv:2405.12967v3; to appear in Cambridge J. Math.. [arXiv]

S. Mondal, Zeta Function of F-Gauges and Special Values, arXiv:2501.05027v1. [arXiv]

N. Riggenbach, K-Theory of Truncated Polynomials, Math. Z. 310, Article 59. [arXiv]

A. N. Skorobogatov, Boundedness of the p-Primary Torsion of the Brauer Group of Products of Varieties, Forum Math. Sigma 13, e134. [arXiv]

F. Wagner, q-Witt Vectors and q-Hodge Complexes, arXiv:2410.23078v5. [arXiv]

B. Bhatt, A. Mathew, and V. Vologodsky, Sheared Witt Vectors, arXiv:2607.01178v1. [arXiv]

L. Illusie, Recent Developments on Zeta Values over Finite Fields, after S. Mondal, author manuscript, 52 pp.. [PDF]

S. Li and Y. Yang, On de Rham–Witt Cohomology of Classifying Stacks, arXiv:2604.03062v1. [arXiv]

S. Mondal and M. Olsson, Height 1 Group Schemes and Prismatic F-Gauges, arXiv:2604.16066v1. [arXiv]

S. Mondal, Syntomic Cohomology of Rational Weights and Zeta Functions, author manuscript. [PDF]

S. Mondal and E. Reinecke, Unipotent Homotopy Theory of Schemes, J. Amer. Math. Soc. 39, 205–312. [arXiv]

Y. Yang, Remarks on p-Primary Torsion of the Brauer Group, J. Number Theory 279, 184–215. [DOI] [arXiv v2]

Y. Zhang, Higher Dimensional Dominoes in de Rham–Witt Cohomology, arXiv:2607.26323v1. [arXiv]