Article
| Title: | Some remarks on plectic motivic spaces and spectra (English) |
| Author: | Hu, Po |
| Author: | Kriz, Daniel |
| Author: | Kriz, Igor |
| Author: | Somberg, Petr |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 2 |
| Year: | 2025 |
| Pages: | 585-598 |
| Summary lang: | English |
| . | |
| Category: | math |
| . | |
| Summary: | We formulate a motivic homotopy theory version of the plectic conjecture of J. Nekovář and A. J. Scholl and give some initial discussion of it. (English) |
| Keyword: | plectic structure |
| Keyword: | motivic homotopy theory |
| Keyword: | norm map |
| Keyword: | Shimura variety |
| MSC: | 14F42 |
| MSC: | 14G35 |
| DOI: | 10.21136/CMJ.2025.0328-24 |
| . | |
| Date available: | 2025-05-20T11:47:48Z |
| Last updated: | 2025-05-26 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152959 |
| . | |
| Reference: | [1] Bachmann, T., Hoyois, M.: Norms in Motivic Homotopy Theory.Astérisque 425. Société Mathématique de France, Paris (2021). Zbl 1522.14028, MR 4288071, 10.24033/ast.1147 |
| Reference: | [2] Davidescu, C., Scholl, A. J.: Extensions in the cohomology of Hilbert modular varieties.Münster J. Math. 13 (2020), 509-518. Zbl 1469.11193, MR 4130690, 10.17879/90169645603 |
| Reference: | [3] Deligne, P.: Théorie de Hodge II.Publ. Math., Inst. Hautes Étud. Sci. 40 (1971), 5-57 French. Zbl 0219.14007, MR 0498551, 10.1007/BF02684692 |
| Reference: | [4] Deligne, P.: Travaux de Shimura.Séminaire N. Bourbaki Lecture Notes in Mathematics 244. Springer, Berlin (1971), 123-165 French. Zbl 0225.14007, MR 0498581, 10.1007/BFb0058700 |
| Reference: | [5] Faltings, G.: Arithmetische Kompaktifizierung des Modulraums der abelschen Varietäten.Arbeitstagung Bonn 1984 Lecture Notes in Mathematics 1111. Springer, Berlin (1985), 321-383 German. Zbl 0597.14036, MR 0797429, 10.1007/BFb0084598 |
| Reference: | [6] Harder, G.: On the cohomology of $SL(2,O)$.Lie Groups and Their Representations Halsted Press, New York (1975), 139-150. Zbl 0395.57028, MR 0425019 |
| Reference: | [7] Hu, P.: Base change functors in the $\Bbb{A}^1$-stable homotopy category.Homology Homotopy Appl. 3 (2001), 417-451. Zbl 1012.55017, MR 1856035, 10.4310/HHA.2001.v3.n2.a8 |
| Reference: | [8] Jardine, J. F.: Simplicial presheaves.J. Pure. Appl. Algebra 47 (1987), 35-87. Zbl 0624.18007, MR 0906403, 10.1016/0022-4049(87)90100-9 |
| Reference: | [9] Jardine, J. F.: Motivic symmetric spectra.Doc. Math. 5 (2000), 445-553. Zbl 0969.19004, MR 1787949, 10.4171/DM/86 |
| Reference: | [10] Morel, F., Voevodsky, V.: $\Bbb{A}^1$-homotopy theory of schemes.Publ. Math., Inst. Hautes Étud. Sci. 90 (1999), 45-143. Zbl 0983.14007, MR 1813224, 10.1007/BF02698831 |
| Reference: | [11] Mumford, D.: Geometric Invariant Theory.Ergebnisse der Mathematik und ihrer Grenzgebiete 34. Springer, Berlin (1965). Zbl 0147.39304, MR 0214602 |
| Reference: | [12] Nekovář, J., Scholl, A. J.: Introduction to plectic cohomology.Advances in the Theory of Automorphic Forms and Their $L$-Functions Contemporary Mathematics 664. AMS, Providence (2016), 321-337. Zbl 1402.11092, MR 3502988, 10.1090/conm/664 |
| Reference: | [13] Nekovář, J., Scholl, A. J.: Plectic Hodge theory I.Available at \brokenlink{http://dx.doi.org/{10.17863/CAM.39172}} (2017). 10.17863/CAM.39172 |
| Reference: | [14] Rapoport, M.: Compactifications de l'espace de modules de Hilbert-Blumenthal.Compos. Math. 36 (1978), 255-335 French. Zbl 0386.14006, MR 0515050 |
| Reference: | [15] Geer, G. van der: Hilbert Modular Surfaces.Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Bd. 16. Springer, Berlin (1988). Zbl 0634.14022, MR 0930101, 10.1007/978-3-642-61553-5 |
| . |
Fulltext not available (moving wall 24 months)
Search
Partner of
