Abstract
Given a field k of characteristic different from 2 and an integer d ≥ 3, let J be the Jacobian of the “generic” hyperelliptic curve given by
(Communicated by Filippo Nuccio)
Acknowledgement
The author would like to thank the referee for a number of corrections and suggestions which have improved this text.
References
[1] A’Campo, N.: Tresses, monodromie et le groupe symplectique, Comment. Math. Helv. 54(1) (1979), 318–327.10.1007/BF02566275Search in Google Scholar
[2] Anni, S.—Dokchitser, V.: Constructing hyperelliptic curves with surjective Galois representations, arXiv:1701.05915 (2017).10.1090/tran/7995Search in Google Scholar
[3] Birman, J. S.: Braids, Links, and Mapping Class Groups. Ann. of Math. Stud. 82, 1974.10.1515/9781400881420Search in Google Scholar
[4] Brumer, A.—Kramer, K.: Large 2-adic galois image and non-existence of certain abelian surfaces over Q, arXiv:1701.01890 (2017).10.4064/aa170514-20-2Search in Google Scholar
[5] Dokchitser, T.—Dokchitser, V.: Regulator constants and the parity conjecture, Invent. Math. 178(1) (2009), 23–71.10.1007/s00222-009-0193-7Search in Google Scholar
[6] Grothendieck, A.—Raynaud, M.: Modeles de néron et monodromie. In: Groupes de Monodromie en Géométrie Algébrique, Springer, 1972, pp. 313–523.10.1007/BFb0068694Search in Google Scholar
[7] Hasson, H.—Yelton, J.: Prime-to- p étale fundamental groups of punctured projective lines over strictly henselian fields, arXiv:1707.00649 (2017).10.1090/tran/7865Search in Google Scholar
[8] Milne, J. S.: Abelian varieties. In: Arithmetic Geometry, Springer, 1986, pp. 103–150.10.1007/978-1-4613-8655-1_5Search in Google Scholar
[9] Milne, J. S.: Jacobian varieties. In: Arithmetic Geometry, Springer, 1986, pp. 167–212.10.1007/978-1-4613-8655-1_7Search in Google Scholar
[10] Mumford, D.: Tata lectures on theta II. Progr. Math. 43, 1984.10.1007/978-0-8176-4578-6Search in Google Scholar
[11] Sato, M.: The abelianization of the level d mapping class group, J. Topol. 3(4) (2010), 847–882.10.1112/jtopol/jtq026Search in Google Scholar
[12] Serre, J.-P.—Tate, J.: Good reduction of abelian varieties, Ann. Math. (1968), 492–517.10.1007/978-3-642-37726-6_79Search in Google Scholar
[13] Wagner, A.: The faithful linear representation of least degree of Sn and An over a field of characteristic 2, Math. Z. 151(2) (1976), 127–137.10.1007/BF01213989Search in Google Scholar
[14] Yelton, J.: Dyadic torsion of elliptic curves, Eur. J. Math. 1(4) (2015), 704–716.10.1007/s40879-015-0055-3Search in Google Scholar
[15] Yelton, J.: Images of 2-adic representations associated to hyperelliptic Jacobians, J. Number Theory 151 (2015), 7–17.10.1016/j.jnt.2014.10.020Search in Google Scholar
[16] Yelton, J.: A note on 8-division fields of elliptic curves, Eur. J. Math. 3 (2017), 603–613.10.1007/s40879-017-0162-4Search in Google Scholar
[17] Yu, J.-K.: Toward a Proof of the Cohen-Lenstra Conjecture in the Function Field Case, Université Bordeaux I-A2X, 351, 1996.Search in Google Scholar
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