Geometry & Topology Volume 28, issue 2 (2024)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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On the top-weight rational cohomology of $\mathcal{A}_g$

Madeline Brandt, Juliette Bruce, Melody Chan, Margarida Melo, Gwyneth Moreland and Corey Wolfe

Geometry & Topology 28 (2024) 497–538

DOI: 10.2140/gt.2024.28.497

Bibliography

1	D Abramovich, L Caporaso, S Payne, The tropicalization of the moduli space of curves, Ann. Sci. Éc. Norm. Supér. 48 (2015) 765 MR3377065
2	V Alexeev, A Brunyate, Extending the Torelli map to toroidal compactifications of Siegel space, Invent. Math. 188 (2012) 175 MR2897696
3	D Allcock, D Corey, S Payne, Tropical moduli spaces as symmetric Δ–complexes, Bull. Lond. Math. Soc. 54 (2022) 193 MR4396931
4	A Ash, D Mumford, M Rapoport, Y Tai, Smooth compactification of locally symmetric varieties, 4, Math. Sci. Press (1975) MR0457437
5	W L Baily Jr., A Borel, Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math. 84 (1966) 442 MR0216035
6	A Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. 7 (1974) 235 MR0387496
7	A Borel, J P Serre, Corners and arithmetic groups, Comment. Math. Helv. 48 (1973) 436 MR0387495
8	S Brannetti, M Melo, F Viviani, On the tropical Torelli map, Adv. Math. 226 (2011) 2546 MR2739784
9	F Brown, Mixed Tate motives over ℤ, Ann. of Math. 175 (2012) 949 MR2993755
10	B Brück, J Miller, P Patzt, R J Sroka, J C H Wilson, On the codimension-two cohomology of SL_n(ℤ), preprint (2022) arXiv:2204.11967
11	M Chan, Combinatorics of the tropical Torelli map, Algebra Number Theory 6 (2012) 1133 MR2968636
12	M Chan, S Galatius, S Payne, Tropical curves, graph complexes, and top weight cohomology of ℳ_g, J. Amer. Math. Soc. 34 (2021) 565 MR4280867
13	M Chan, M Melo, F Viviani, Tropical Teichmüller and Siegel spaces, from: "Algebraic and combinatorial aspects of tropical geometry" (editors E Brugallé, M A Cueto, A Dickenstein, E M Feichtner, I Itenberg), Contemp. Math. 589, Amer. Math. Soc. (2013) 45 MR3088910
14	R Charney, R Lee, Cohomology of the Satake compactification, Topology 22 (1983) 389 MR0715247
15	J Chen, E Looijenga, The stable cohomology of the Satake compactification of 𝒜_g, Geom. Topol. 21 (2017) 2231 MR3654107
16	T Church, B Farb, A Putman, A stability conjecture for the unstable cohomology of SL_nℤ, mapping class groups, and Aut(F_n), from: "Algebraic topology: applications and new directions" (editors U Tillmann, S r Galatius, D Sinha), Contemp. Math. 620, Amer. Math. Soc. (2014) 55 MR3290086
17	T Church, A Putman, The codimension-one cohomology of SL_nℤ, Geom. Topol. 21 (2017) 999 MR3626596
18	D A Cox, J B Little, H K Schenck, Toric varieties, 124, Amer. Math. Soc. (2011) MR2810322
19	P Deligne, Théorie de Hodge, II, Inst. Hautes Études Sci. Publ. Math. 40 (1971) 5 MR0498551
20	P Deligne, Théorie de Hodge, III, Inst. Hautes Études Sci. Publ. Math. 44 (1974) 5 MR0498552
21	M Dutour Sikirić, P Elbaz-Vincent, A Kupers, J Martinet, Voronoi complexes in higher dimensions, cohomology of GL_N(Z) for N ≥ 8 and the triviality of K₈(Z), preprint (2019) arXiv:1910.11598
22	P Elbaz-Vincent, H Gangl, C Soulé, Perfect forms, K–theory and the cohomology of modular groups, Adv. Math. 245 (2013) 587 MR3084439
23	G Faltings, C L Chai, Degeneration of abelian varieties, 22, Springer (1990) MR1083353
24	S Grushevsky, Geometry of 𝒜_g and its compactifications, from: "Algebraic geometry, I" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80.1, Amer. Math. Soc. (2009) 193 MR2483936
25	S Grushevsky, K Hulek, O Tommasi, Stable Betti numbers of (partial) toroidal compactifications of the moduli space of abelian varieties, from: "Geometry and physics, II" (editors J E Andersen, A Dancer, O García-Prada), Oxford Univ. Press (2018) 581 MR3931788
26	S Grushevsky, K Hulek, O Tommasi, Stable cohomology of the perfect cone toroidal compactification of 𝒜_g, J. Reine Angew. Math. 741 (2018) 211 MR3836148
27	R Hain, The rational cohomology ring of the moduli space of abelian 3–folds, Math. Res. Lett. 9 (2002) 473 MR1928867
28	F Harary, M J Piff, D J A Welsh, On the automorphism group of a matroid, Discrete Math. 2 (1972) 163 MR0297639
29	G Harder, A Gauss–Bonnet formula for discrete arithmetically defined groups, Ann. Sci. École Norm. Sup. 4 (1971) 409 MR0309145
30	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
31	K Hulek, O Tommasi, Cohomology of the second Voronoi compactification of 𝒜₄, Doc. Math. 17 (2012) 195 MR2946823
32	K Hulek, O Tommasi, The topology of 𝒜_g and its compactifications, from: "Geometry of moduli" (editors J A Christophersen, K Ranestad), Abel Symp. 14, Springer (2018) 135 MR3968046
33	J Igusa, On Siegel modular forms of genus two, Amer. J. Math. 84 (1962) 175 MR0141643
34	D O Jaquet-Chiffelle, Énumération complète des classes de formes parfaites en dimension 7, Ann. Inst. Fourier (Grenoble) 43 (1993) 21 MR1209694
35	R Lee, R H Szczarba, On the homology and cohomology of congruence subgroups, Invent. Math. 33 (1976) 15 MR0422498
36	R Lee, R H Szczarba, On the torsion in K₄(ℤ) and K₅(ℤ), Duke Math. J. 45 (1978) 101 MR0491893
37	M Melo, F Viviani, Comparing perfect and 2nd Voronoi decompositions : the matroidal locus, Math. Ann. 354 (2012) 1521 MR2993003
38	Y Namikawa, Toroidal compactification of Siegel spaces, 812, Springer (1980) MR0584625
39	Y Odaka, Tropical geometric compactification of moduli, II : A_g case and holomorphic limits, Int. Math. Res. Not. 2019 (2019) 6614 MR4027562
40	Y Odaka, Y Oshima, Collapsing K3 surfaces, tropical geometry and moduli compactifications of Satake, Morgan–Shalen type, 40, Math. Soc. Japan (2021) MR4290084
41	J G Oxley, Matroid theory, Oxford Univ. Press (1992) MR1207587
42	N I Shepherd-Barron, Perfect forms and the moduli space of abelian varieties, Invent. Math. 163 (2006) 25 MR2208417
43	C Soulé, On the 3–torsion in K₄(ℤ), Topology 39 (2000) 259 MR1722032
44	G Voronoi, Nouvelles applications des paramètres continus à la théorie des formes quadratiques, I : Sur quelques propriétés des formes quadratiques positives parfaites, J. Reine Angew. Math. 133 (1908) 97 MR1580737
45	H Whitney, Congruent graphs and the connectivity of graphs, Amer. J. Math. 54 (1932) 150 MR1506881
46	T Willwacher, M Kontsevich’s graph complex and the Grothendieck–Teichmüller Lie algebra, Invent. Math. 200 (2015) 671 MR3348138