Volume 9 (2026)
Antieau, Benjamin
Spectral sequences, décalage, and the Beilinson $t$-structure
Annales Henri Lebesgue, Volume 9 (2026), pp. 885-927

Metadata

DOI10.5802/ahl.278
Keywords spectral sequences ,  $t$-structures

Abstract

This paper explains the theory of spectral sequences via décalage and the Beilinson $t$-structure.


References

[1] Antieau, Benjamin; Gepner, David; Heller, Jeremiah <span class="mathjax-formula formula-with-tex" data-tex="\({K}\)">\({K}\)</span>-theoretic obstructions to bounded <span class="mathjax-formula formula-with-tex" data-tex="\(t\)">\(t\)</span>-structures, Invent. Math., Volume 216 (2019) no. 1, pp. 241-300 | DOI | MR | Zbl

[2] Ayala, David; Mazel-Gee, Aaron; Rozenblyum, Nick Stratified noncommutative geometry, Memoirs of the American Mathematical Society, 1485, American Mathematical Society, 2024, iii+260 pages | DOI | MR | Zbl

[3] Antieau, Benjamin; Nikolaus, Thomas Cartier modules and cyclotomic spectra, J. Am. Math. Soc., Volume 34 (2021) no. 1, pp. 1-78 | DOI | MR | Zbl

[4] Antieau, Benjamin Periodic cyclic homology and derived de Rham cohomology, Ann. <span class="mathjax-formula formula-with-tex" data-tex=""></span>-Theory, Volume 4 (2019) no. 3, pp. 505-519 | DOI | MR | Zbl

[5] Ariotta, Stefano Coherent cochain complexes and Beilinson t-structures, with an appendix by Achim Krause (2021) | arXiv

[6] Beilinson, Alexander A. On the derived category of perverse sheaves, <span class="mathjax-formula formula-with-tex" data-tex="\({K}\)">\({K}\)</span>-theory, arithmetic and geometry (Moscow, 1984–1986) (Lecture Notes in Mathematics), Volume 1289, Springer, 1987, pp. 27-41 | DOI | MR | Zbl

[7] Bhatt, Bhargav; Morrow, Matthew; Scholze, Peter Topological Hochschild homology and integral <span class="mathjax-formula formula-with-tex" data-tex="\(p\)">\(p\)</span>-adic Hodge theory, Publ. Math., Inst. Hautes Étud. Sci., Volume 129 (2019), pp. 199-310 | DOI | MR | Zbl

[8] Boardman, J. Michael Conditionally convergent spectral sequences, Homotopy invariant algebraic structures (Baltimore, MD, 1998) (Contemporary Mathematics), Volume 239, American Mathematical Society, 1999, pp. 49-84 | DOI | MR | Zbl

[9] Cirici, Joana; Egas Santander, Daniela; Livernet, Muriel; Whitehouse, Sarah Model category structures and spectral sequences, Proc. R. Soc. Edinb., Sect. A, Math., Volume 150 (2020) no. 6, pp. 2815-2848 | DOI | MR | Zbl

[10] Cirici, Joana; Guillén, Francisco Homotopy theory of mixed Hodge complexes, Tôhoku Math. J. (2), Volume 68 (2016) no. 3, pp. 349-375 | DOI | MR | Zbl

[11] Clausen, Dustin; Mathew, Akhil Hyperdescent and étale <span class="mathjax-formula formula-with-tex" data-tex="\({K}\)">\({K}\)</span>-theory, Invent. Math., Volume 225 (2021) no. 3, pp. 981-1076 | DOI | MR | Zbl

[12] Deligne, Pierre Théorie de Hodge. II, Publ. Math., Inst. Hautes Étud. Sci., Volume 40 (1971), pp. 5-57 | DOI | MR | Zbl | Numdam

[13] Deligne, Pierre Théorie de Hodge. III, Publ. Math., Inst. Hautes Étud. Sci., Volume 44 (1974), pp. 5-77 | MR | Zbl | Numdam | DOI

[14] Gheorghe, Bogdan; Isaksen, Daniel C.; Krause, Achim; Ricka, Nicolas <span class="mathjax-formula formula-with-tex" data-tex="\(\mathbb{C}\)">\(\mathbb{C}\)</span>-motivic modular forms, J. Eur. Math. Soc., Volume 24 (2022) no. 10, pp. 3597-3628 | DOI | MR | Zbl

[15] Glasman, Saul Day convolution for <span class="mathjax-formula formula-with-tex" data-tex="\(\infty \)">\(\infty \)</span>-categories, Math. Res. Lett., Volume 23 (2016) no. 5, pp. 1369-1385 | DOI | MR | Zbl

[16] Gwilliam, Owen; Pavlov, Dmitri Enhancing the filtered derived category, J. Pure Appl. Algebra, Volume 222 (2018) no. 11, pp. 3621-3674 | DOI | MR | Zbl

[17] Hedenlund, Alice Multiplicative Tate spectral sequences, University of Oslo, Norway (2020)

[18] Hahn, Jeremy; Raksit, Arpon; Wilson, Dylan A motivic filtration on the topological cyclic homology of commutative ring spectra (2022) | arXiv

[19] Joyal, André Notes on quasi-categories (2008)

[20] Lawson, Tyler Filtered spaces, filtered objects (2024) | arXiv

[21] Levine, Marc The Adams-Novikov spectral sequence and Voevodsky’s slice tower, Geom. Topol., Volume 19 (2015) no. 5, pp. 2691-2740 | DOI | MR | Zbl

[22] Lurie, Jacob Rotation invariance in algebraic <span class="mathjax-formula formula-with-tex" data-tex="\({K}\)">\({K}\)</span>-theory, 2015

[23] Lurie, Jacob Higher Algebra, 2017

[24] Lurie, Jacob Spectral algebraic geometry, 2018

[25] Livernet, Muriel; Whitehouse, Sarah Spectral sequences via linear presheaves (2024) | arXiv

[26] Maunder, C. R. F. The spectral sequence of an extraordinary cohomology theory, Proc. Camb. Philos. Soc., Volume 59 (1963), pp. 567-574 | DOI | MR | Zbl

[27] McCleary, John A user’s guide to spectral sequences, Cambridge Studies in Advanced Mathematics, 58, Cambridge University Press, 2001, xvi+561 pages | MR | Zbl

[28] Mor, Itamar Picard and Brauer groups of <span class="mathjax-formula formula-with-tex" data-tex="\({K}(n)\)">\({K}(n)\)</span>-local spectra via profinite Galois descent (2023) | arXiv

[29] Moulinos, Tasos The geometry of filtrations, Bull. Lond. Math. Soc., Volume 53 (2021) no. 5, pp. 1486-1499 | DOI | MR | Zbl

[30] Pstrągowski, Piotr Synthetic spectra and the cellular motivic category, Invent. Math., Volume 232 (2023) no. 2, pp. 553-681 | DOI | MR | Zbl

[31] Raksit, Arpon Hochschild homology and the derived de Rham complex revisited (2020) | arXiv

[32] Weibel, Charles A. An introduction to homological algebra, Cambridge Studies in Advanced Mathematics, 38, Cambridge University Press, 1994, xiv+450 pages | DOI | MR | Zbl