Geometry & Topology Volume 29, issue 5 (2025)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Big monodromy for higher Prym representations

Aaron Landesman, Daniel Litt and Will Sawin

Geometry & Topology 29 (2025) 2733–2782

DOI: 10.2140/gt.2025.29.2733

Bibliography

1	D Abramovich, A Corti, A Vistoli, Twisted bundles and admissible covers, Comm. Algebra 31 (2003) 3547 MR2007376
2	N A’Campo, Tresses, monodromie et le groupe symplectique, Comment. Math. Helv. 54 (1979) 318 MR535062
3	J D Achter, Results of Cohen–Lenstra type for quadratic function fields, from: "Computational arithmetic geometry" (editors K E Lauter, K A Ribet), Contemp. Math. 463, Amer. Math. Soc. (2008) 1 MR2459984
4	Y André, Mumford–Tate groups of mixed Hodge structures and the theorem of the fixed part, Compos. Math. 82 (1992) 1 MR1154159
5	M F Atiyah, The signature of fibre-bundles, from: "Global analysis" (editors D C Spencer, S Iyanaga), Univ. Tokyo Press (1969) 73 MR254864
6	J Bertin, M Romagny, Champs de Hurwitz, 125-126, Soc. Math. France (2011) 219 MR2920693
7	J Carlson, M Green, P Griffiths, J Harris, Infinitesimal variations of Hodge structure, I, Compos. Math. 50 (1983) 109 MR720288
8	C C Chevalley, The algebraic theory of spinors, Columbia Univ. Press (1954) MR60497
9	A Collino, G P Pirola, The Griffiths infinitesimal invariant for a curve in its Jacobian, Duke Math. J. 78 (1995) 59 MR1328752
10	P Deligne, Variétés de Shimura : interprétation modulaire, et techniques de construction de modèles canoniques, from: "Automorphic forms, representations and L-functions, II" (editors A Borel, W Casselman), Proc. Sympos. Pure Math. 33, Amer. Math. Soc. (1979) 247 MR546620
11	P Deligne, G D Mostow, Monodromy of hypergeometric functions and nonlattice integral monodromy, Inst. Hautes Études Sci. Publ. Math. 63 (1986) 5 MR849651
12	P Deligne, J S Milne, A Ogus, K y Shih, Hodge cycles, motives, and Shimura varieties, 900, Springer (1982) MR654325
13	N M Dunfield, W P Thurston, Finite covers of random 3-manifolds, Invent. Math. 166 (2006) 457 MR2257389
14	J S Ellenberg, A Venkatesh, C Westerland, Homological stability for Hurwitz spaces and the Cohen–Lenstra conjecture over function fields, Ann. of Math. 183 (2016) 729 MR3488737
15	B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
16	M D Fried, H Völklein, The inverse Galois problem and rational points on moduli spaces, Math. Ann. 290 (1991) 771 MR1119950
17	F Grunewald, M Larsen, A Lubotzky, J Malestein, Arithmetic quotients of the mapping class group, Geom. Funct. Anal. 25 (2015) 1493 MR3426060
18	J Harris, An introduction to infinitesimal variations of Hodge structures, from: "Workshop Bonn 1984" (editors F Hirzebruch, J Schwermer, S Suter), Lecture Notes in Math. 1111, Springer (1985) 51 MR797415
19	N V Ivanov, Fifteen problems about the mapping class groups, from: "Problems on mapping class groups and related topics" (editor B Farb), Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 71 MR2264532
20	L Jain, Big mod ℓ monodromy for families of G covers, PhD thesis, University of Wisconsin–Madison (2016) MR3553614
21	N M Katz, Exponential sums and differential equations, 124, Princeton Univ. Press (1990) MR1081536
22	K Kodaira, A certain type of irregular algebraic surfaces, J. Anal. Math. 19 (1967) 207 MR216521
23	E Looijenga, Prym representations of mapping class groups, Geom. Dedicata 64 (1997) 69 MR1432535
24	E Looijenga, Arithmetic representations of mapping class groups, Algebr. Geom. Topol. 25 (2025) 677
25	V Marković, Unramified correspondences and virtual properties of mapping class groups, Bull. Lond. Math. Soc. 54 (2022) 2324 MR4549123
26	C T McMullen, Braid groups and Hodge theory, Math. Ann. 355 (2013) 893 MR3020148
27	V B Mehta, C S Seshadri, Moduli of vector bundles on curves with parabolic structures, Math. Ann. 248 (1980) 205 MR575939
28	B Moonen, Families of motives and the Mumford–Tate conjecture, Milan J. Math. 85 (2017) 257 MR3735565
29	A N Parshin, Algebraic curves over function fields, I, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968) 1191 MR257086
30	E Samperton, Schur-type invariants of branched G-covers of surfaces, from: "Topological phases of matter and quantum computation" (editors P Bruillard, C Ortiz Marrero, J Plavnik), Contemp. Math. 747, Amer. Math. Soc. (2020) 173 MR4079751
31	E Sernesi, Deformations of algebraic schemes, 334, Springer (2006) MR2247603
32	T N Venkataramana, Image of the Burau representation at d-th roots of unity, Ann. of Math. 179 (2014) 1041 MR3171758
33	T N Venkataramana, Monodromy of cyclic coverings of the projective line, Invent. Math. 197 (2014) 1 MR3219513
34	C Voisin, Schiffer variations and the generic Torelli theorem for hypersurfaces, Compos. Math. 158 (2022) 89 MR4379048
35	S Wewers, Construction of Hurwitz spaces, PhD thesis, University of Essen (1998)
36	M M Wood, An algebraic lifting invariant of Ellenberg, Venkatesh, and Westerland, Res. Math. Sci. 8 (2021) 21 MR4240808
37	K Yokogawa, Infinitesimal deformation of parabolic Higgs sheaves, Int. J. Math. 6 (1995) 125 MR1307307
38	Y G Zarkhin, Weights of simple Lie algebras in the cohomology of algebraic varieties, Izv. Akad. Nauk SSSR Ser. Mat. 48 (1984) 264 MR740792