Smooth weight structures and birationality filtrations on motivic categories

M. V. Bondarko ; D. Z. Kumallagov

Algebra i analiz, Tome 33 (2021) no. 5, pp. 51-79.

Bibliographie

[1] Alonso L., Jeremías A., Souto M. J., “Construction of t-structures and equivalences of derived categories”, Trans. Amer. Math. Soc., 355:6 (2003), 2523–2543 | DOI | MR | Zbl

[2] Ananyevskiy A., Neshitov A., “Framed and MW-transfers for homotopy modules”, Selecta Math. N. S., 25:2 (2019), 26 | DOI | MR | Zbl

[3] Asok A., “Birational invariants and $\mathbb{A}^{1}$-connectedness”, J. Reine Angew. Math., 681 (2013), 39–64 | MR | Zbl

[4] Ayoub J., Les six opérations de Grothendieck et le formalisme des cycles évanescents dans le monde motivique (I), Astérisque, 314, Soc. Math. France, 2007 | MR

[5] Bachmann T., “On the conservativity of the functor assigning to a motivic spectrum its motive”, Duke Math. J., 167:8 (2018), 1525–1571 | DOI | MR | Zbl

[6] Bachmann T., Hana Jia Kong, Guozhen Wang, Zhouli Xu, The Chow t-structure on motivic spectra, 2020, arXiv: 2012.02687

[7] Bachmann T., Yakerson M., “Towards conservativity of $\mathbb{G}_m$-stabilization”, Geom. Topol., 24:4 (2020), 1969–2034 | DOI | MR | Zbl

[8] Beilinson A., Bernstein J., Deligne P., “Faisceaux pervers”, Asterisque, 100, Soc. Math. France, Paris, 1982, 5–171 | MR

[9] Bondarko M. V., “Weight structures vs. $t$-structures; weight filtrations, spectral sequences, and complexes (for motives and in general)”, J. K-theory, 6:3 (2010), 387–504 | DOI | MR | Zbl

[10] Bondarko M. V., “Motivically functorial coniveau spectral sequences; direct summands of cohomology of function fields”, Doc. Math., 2010, Extra vol.: A. Suslin's Sixtieth Birthday, 33–117 | MR | Zbl

[11] Bondarko M. V., “$\mathbb{Z}[\frac{1}{p}]$-motivic resolution of singularities”, Compositio Math., 147:5 (2011), 1434–1446 | DOI | MR | Zbl

[12] Bondarko M. V., Gersten weight structures for motivic homotopy categories; retracts of cohomology of function fields, motivic dimensions, and coniveau spectral sequences, 2018, arXiv: 1803.01432

[13] Bondarko M. V., “On weight complexes, pure functors, and detecting weights”, J. Algebra, 574 (2021), 617–668 | DOI | MR | Zbl

[14] Bondarko M. V., From weight structures to (orthogonal) $t$-structures and back, 2019, arXiv: 1907.03686 | MR

[15] Bondarko M. V., “On infinite effectivity of motivic spectra and the vanishing of their motives”, Doc. Math., 25 (2020), 811–840 | MR | Zbl

[16] Bondarko M. V., On Chow-pure cohomology and Euler characteristics for motives and varieties, and their relation to unramified cohomology and Brauer groups, 2020, arXiv: 2003.10415

[17] Bondarko M. V., Déglise F., “Dimensional homotopy $t$-structures in motivic homotopy theory”, Adv. Math., 311 (2017), 91–189 | DOI | MR | Zbl

[18] Bondarko M. V., Kumallagov D. Z., “Vesovye struktury Chzhou bez proektivnosti i razresheniya osobennostei”, Algebra i analiz, 30:5 (2018), 57–83

[19] Bondarko M. V., Kumallagov D. Z., “Chzhou-vesovye gomologii motivnykh kompleksov i ikh svyaz s motivnymi gomologiyami”, Vestn. S.-Peterburg. gos. un-ta. Ser. mat. mekh. astronom., 2020, no. 4, 560–587 | MR | Zbl

[20] Bondarko M. V., Sosnilo V. A., “On purely generated $\alpha$-smashing weight structures and weight-exact localizations”, J. Algebra, 535 (2019), 407–455 | DOI | MR | Zbl

[21] Bondarko M. V., Sosnilo V. A., “On constructing weight structures and extending them to idempotent extensions”, Homology, Homotopy Appl., 20:1 (2018), 37–57 | DOI | MR | Zbl

[22] Bondarko M. V., Sosnilo V. A., On Chow-weight homology of geometric motives, Trans. Amer. Math. Soc., 2020 (to appear); arXiv: 1411.6354

[23] Cisinski D.-C., Déglise F., Triangulated categories of mixed motives, Springer Monogr. Math., Springer, Cham, 2019 | DOI | MR | Zbl

[24] Colliot-ThéléneJ.-L., Hoobler R. T., Kahn B., “The Bloch–Ogus–Gabber theorem”, Algebraic K-theory (Toronto, ON, 1996), Fields Inst. Commun., 16, Amer. Math. Soc., Providence, RI, 1997, 31–94 | MR

[25] Déglise F., “Modules homotopiques”, Homotopy modules, Doc. Math., 16, 2011, 411–455 | MR | Zbl

[26] Déglise F., “Orientable homotopy modules”, Amer. J. Math., 135:2 (2013), 519–560 | DOI | MR | Zbl

[27] Garkusha G., Panin I., “Homotopy invariant presheaves with framed transfers”, Cambridge J. Math., 8:1 (2020), 1–94 | DOI | MR | Zbl

[28] Hoyois M., “From algebraic cobordism to motivic cohomology”, J. Reine Angew. Math., 702 (2015), 173–226 | MR | Zbl

[29] Kahn B., Sujatha R., “Birational motives, II: triangulated birational motives”, Int. Math. Res. Not. IMRN, 22:22 (2017), 6778–6831 | MR | Zbl

[30] Levine M., “Convergence of Voevodsky's slice tower”, Doc. Math., 18 (2013), 907–941 | MR | Zbl

[31] Morel F., “An introduction to $A^1$-homotopy theory”, Contemporary Developments in Algebraic K-theory, ICTP Lect. Notes, XV, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2004, 357–441 | MR

[32] Morel F., “The stable $A^1$-connectivity theorems”, K-theory, 35:1-2 (2005), 1–68 | DOI | MR | Zbl

[33] Neeman A., Triangulated categories, Ann. Math. Stud., 148, Princeton Univ. Press, Princeton, NJ, 2001 | MR | Zbl

[34] Pauksztello D., “A note on compactly generated co-t-structures”, Comm. Algebra, 40:2 (2012), 386–394 | DOI | MR | Zbl

[35] Pelaez P., “Birational motivic homotopy theories and the slice filtration”, Doc. Math., 18 (2013), 51–70 | MR | Zbl

[36] Pelaez P., “Mixed motives and motivic birational covers”, J. Pure Appl. Algebra, 221:7 (2017), 1699–1716 | DOI | MR | Zbl

[37] Voevodsky V., “Triangulated category of motives”, Ann. Math. Stud., 143, Princeton Univ. Press, Princeton, NJ, 2000, 188–238 | Zbl

[38] Voevodsky V., “Cohomological theory of presheaves with transfers”, Ann. Math. Stud., 143, Princeton Univ. Press, Princeton, 2000, 87–137 | MR | Zbl