The Nisnevich motive of an algebraic stack. (English) Zbl 1524.14047
Summary: We construct the motive of an algebraic stack in the Nisnevich topology. For stacks which are Nisnevich locally quotient stacks, we give a presentation of the motive in terms of simplicial schemes. We also show that the motivic cohomology agrees with the Chow groups of Edidin-Graham-Totaro with integer coefficients.
MSC:
| 14F42 | Motivic cohomology; motivic homotopy theory |
| 14A20 | Generalizations (algebraic spaces, stacks) |
References:
| [1] | 10.1080/00927872.2022.2082234 · Zbl 1507.14004 · doi:10.1080/00927872.2022.2082234 |
| [2] | 10.5802/aif.2833 · Zbl 1314.14095 · doi:10.5802/aif.2833 |
| [3] | ; Ayoub, Joseph, Les six opérations de Grothendieck et le formalisme des cycles évanescents dans le monde motivique, II. Astérisque, 315 (2007) · Zbl 1153.14001 |
| [4] | 10.1515/crelle-2012-0090 · Zbl 1299.14022 · doi:10.1515/crelle-2012-0090 |
| [5] | 10.1016/0001-8708(86)90081-2 · Zbl 0608.14004 · doi:10.1016/0001-8708(86)90081-2 |
| [6] | ; Bousfield, A. K.; Kan, D. M., Homotopy limits, completions and localizations. Lecture Notes in Math., 304 (1972) · Zbl 0259.55004 |
| [7] | 10.1016/j.aim.2012.08.012 · Zbl 1263.14025 · doi:10.1016/j.aim.2012.08.012 |
| [8] | 10.4310/HHA.2009.v11.n1.a11 · Zbl 1175.18007 · doi:10.4310/HHA.2009.v11.n1.a11 |
| [9] | 10.1006/aima.2001.2014 · Zbl 1009.55011 · doi:10.1006/aima.2001.2014 |
| [10] | 10.1017/S0305004103007175 · Zbl 1045.55007 · doi:10.1017/S0305004103007175 |
| [11] | 10.1007/s002220050214 · Zbl 0940.14003 · doi:10.1007/s002220050214 |
| [12] | 10.1353/ajm.2001.0024 · Zbl 1036.14001 · doi:10.1353/ajm.2001.0024 |
| [13] | 10.14231/2017-026 · Zbl 1412.14002 · doi:10.14231/2017-026 |
| [14] | 10.1515/crelle-2011-0004 · Zbl 1343.14015 · doi:10.1515/crelle-2011-0004 |
| [15] | 10.1090/surv/099 · doi:10.1090/surv/099 |
| [16] | 10.1090/S0002-9939-07-08832-6 · Zbl 1133.14001 · doi:10.1090/S0002-9939-07-08832-6 |
| [17] | 10.1093/qmathj/haaa023 · Zbl 1487.14054 · doi:10.1093/qmathj/haaa023 |
| [18] | 10.1016/j.aim.2016.09.031 · Zbl 1400.14065 · doi:10.1016/j.aim.2016.09.031 |
| [19] | 10.1016/0022-4049(87)90100-9 · Zbl 0624.18007 · doi:10.1016/0022-4049(87)90100-9 |
| [20] | 10.1023/A:1021116524762 · Zbl 1058.14004 · doi:10.1023/A:1021116524762 |
| [21] | 10.1023/A:1021648227488 · Zbl 1073.14519 · doi:10.1023/A:1021648227488 |
| [22] | ; Knutson, Donald, Algebraic spaces. Lecture Notes in Math., 203 (1971) · Zbl 0221.14001 |
| [23] | 10.1007/s002220050351 · Zbl 0938.14003 · doi:10.1007/s002220050351 |
| [24] | 10.1090/pspum/080.1/2483938 · Zbl 1169.14001 · doi:10.1090/pspum/080.1/2483938 |
| [25] | ; Laumon, Gérard; Moret-Bailly, Laurent, Champs algébriques. Ergebnisse der Math. (3), 39 (2000) · Zbl 0945.14005 |
| [26] | ; Mazza, Carlo; Voevodsky, Vladimir; Weibel, Charles, Lecture notes on motivic cohomology. Clay Math. Monographs, 2 (2006) · Zbl 1115.14010 |
| [27] | ; Morel, Fabien; Voevodsky, Vladimir, 𝔸1-homotopy theory of schemes, Inst. Hautes Études Sci. Publ. Math., 90, 45 (1999) · Zbl 0983.14007 |
| [28] | 10.1090/tran/7006 · Zbl 1421.14002 · doi:10.1090/tran/7006 |
| [29] | 10.1017/fms.2019.32 · Zbl 1506.14045 · doi:10.1017/fms.2019.32 |
| [30] | 10.1016/j.jalgebra.2014.09.012 · Zbl 1308.14006 · doi:10.1016/j.jalgebra.2014.09.012 |
| [31] | 10.1155/S1073792800000477 · Zbl 1034.14008 · doi:10.1155/S1073792800000477 |
| [32] | 10.1090/pspum/067/1743244 · Zbl 0967.14005 · doi:10.1090/pspum/067/1743244 |
| [33] | 10.1515/crll.2004.2004.577.1 · Zbl 1077.14004 · doi:10.1515/crll.2004.2004.577.1 |
| [34] | 10.1007/BF01388892 · Zbl 0694.14001 · doi:10.1007/BF01388892 |
| [35] | 10.4007/annals.2011.174.1.11 · Zbl 1236.14026 · doi:10.4007/annals.2011.174.1.11 |
| [36] | ; Voevodsky, Vladimir; Suslin, Andrei; Friedlander, Eric M., Cycles, transfers, and motivic homology theories. Annals of Math. Studies, 143 (2000) · Zbl 1021.14006 |
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