Volume 25, issue 7 (2021)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 6, 2483–2999
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
A formula for the Voevodsky motive of the moduli stack of vector bundles on a curve

Victoria Hoskins and Simon Pepin Lehalleur

Geometry & Topology 25 (2021) 3555–3589
Bibliography
1 G Ancona, S Enright-Ward, A Huber, On the motive of a commutative algebraic group, Doc. Math. 20 (2015) 807 MR3398728
2 G Ancona, A Huber, S Pepin Lehalleur, On the relative motive of a commutative group scheme, Algebr. Geom. 3 (2016) 150 MR3477952
3 M F Atiyah, R Bott, The Yang–Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1983) 523 MR702806
4 J Ayoub, Les six opérations de Grothendieck et le formalisme des cycles évanescents dans le monde motivique, I, 314, Soc. Math. France (2007) MR2423375
5 J Ayoub, A guide to (étale) motivic sheaves, from: "Proceedings of the International Congress of Mathematicians, II" (editors S Y Jang, Y R Kim, D W Lee, I Yie), Kyung Moon Sa (2014) 1101 MR3728654
6 J Ayoub, La réalisation étale et les opérations de Grothendieck, Ann. Sci. Éc. Norm. Supér. 47 (2014) 1 MR3205601
7 S del Baño, On the Chow motive of some moduli spaces, J. Reine Angew. Math. 532 (2001) 105 MR1817504
8 M Bagnarol, B Fantechi, F Perroni, On the motive of Quot schemes of zero-dimensional quotients on a curve, New York J. Math. 26 (2020) 138 MR4063954
9 A Beauville, Algebraic cycles on Jacobian varieties, Compos. Math. 140 (2004) 683 MR2041776
10 K Behrend, A Dhillon, On the motivic class of the stack of bundles, Adv. Math. 212 (2007) 617 MR2329314
11 P Belmans, A J de Jong, others, The Stacks project, electronic reference (2005–)
12 A Białynicki-Birula, Some properties of the decompositions of algebraic varieties determined by actions of a torus, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976) 667 MR453766
13 E Bifet, F Ghione, M Letizia, On the Abel–Jacobi map for divisors of higher rank on a curve, Math. Ann. 299 (1994) 641 MR1286890
14 M A A de Cataldo, L Migliorini, The Chow motive of semismall resolutions, Math. Res. Lett. 11 (2004) 151 MR2067464
15 D C Cisinski, F Déglise, Triangulated categories of mixed motives, Springer (2019) MR3971240
16 C Deninger, J Murre, Motivic decomposition of abelian schemes and the Fourier transform, J. Reine Angew. Math. 422 (1991) 201 MR1133323
17 D Edidin, W Graham, Equivariant intersection theory, Invent. Math. 131 (1998) 595 MR1614555
18 R Fedorov, A Soibelman, Y Soibelman, Motivic classes of moduli of Higgs bundles and moduli of bundles with connections, Commun. Number Theory Phys. 12 (2018) 687 MR3904756
19 W Fulton, Intersection theory, 2, Springer (1998) MR1644323
20 D Gaitsgory, J Lurie, Weil’s conjecture for function fields, I, 199, Princeton Univ. Press (2019) MR3887650
21 A Grothendieck, Éléments de géométrie algébrique, IV : Étude locale des schémas et des morphismes de schémas, I, Inst. Hautes Études Sci. Publ. Math. 20 (1964) 5 MR173675
22 A Grothendieck, Éléments de géométrie algébrique, IV : Étude locale des schémas et des morphismes de schémas, II, Inst. Hautes Études Sci. Publ. Math. 24 (1965) 5 MR199181
23 G Harder, Chevalley groups over function fields and automorphic forms, Ann. of Math. 100 (1974) 249 MR563090
24 J Heinloth, A conjecture of Hausel on the moduli space of Higgs bundles on a curve, Astérisque 370, Soc. Math. France (2015) 157 MR3364746
25 J Heinloth, A H W Schmitt, The cohomology rings of moduli stacks of principal bundles over curves, Doc. Math. 15 (2010) 423 MR2657374
26 V Hoskins, S Pepin Lehalleur, On the Voevodsky motive of the moduli stack of vector bundles on a curve, Quart. J. Math. 72 (2021) 71
27 V Hoskins, S Pepin Lehalleur, On the Voevodsky motive of the moduli space of Higgs bundles on a curve, Selecta Math. 27 (2021) MR4222601
28 D Huybrechts, M Lehn, The geometry of moduli spaces of sheaves, Cambridge Univ. Press (2010) MR2665168
29 A Kresch, Cycle groups for Artin stacks, Invent. Math. 138 (1999) 495 MR1719823
30 K Künnemann, On the Chow motive of an abelian scheme, from: "Motives" (editors U Jannsen, S Kleiman, J P Serre), Proc. Sympos. Pure Math. 55, Amer. Math. Soc. (1994) 189 MR1265530
31 G Laumon, Correspondance de Langlands géométrique pour les corps de fonctions, Duke Math. J. 54 (1987) 309 MR899400
32 C Mazza, V Voevodsky, C Weibel, Lecture notes on motivic cohomology, 2, Amer. Math. Soc. (2006) MR2242284
33 B Osserman, Relative dimension of morphisms and dimension for algebraic stacks, J. Algebra 437 (2015) 52 MR3351957
34 S Pepin Lehalleur, Triangulated categories of relative 1–motives, Adv. Math. 347 (2019) 473 MR3920833
35 A T Ricolfi, On the motive of the Quot scheme of finite quotients of a locally free sheaf, J. Math. Pures Appl. 144 (2020) 50 MR4175444
36 B Totaro, The Chow ring of a classifying space, from: "Algebraic K–theory", Proc. Sympos. Pure Math. 67, Amer. Math. Soc. (1999) 249 MR1743244
37 B Totaro, The motive of a classifying space, Geom. Topol. 20 (2016) 2079 MR3548464
38 A Vistoli, Intersection theory on algebraic stacks and on their moduli spaces, Invent. Math. 97 (1989) 613 MR1005008
39 V Voevodsky, Triangulated categories of motives over a field, from: "Cycles, transfers, and motivic homology theories", Ann. of Math. Stud. 143, Princeton Univ. Press (2000) 188 MR1764202