On Euler systems for the multiplicative group over general number fields

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David Burns
King’s College London. Department of Mathematics
Alexandre Daoud
King’s College London. Department of Mathematics
https://orcid.org/0000-0002-9950-1061
Takamichi Sano
Osaka Metropolitan University. Department of Mathematics
https://orcid.org/0000-0002-6991-667X
Soogil Seo
Yonsei University. Department of Mathematics
https://orcid.org/0000-0002-6423-8494

We formulate, and provide strong evidence for, a natural generalization of a conjecture of Robert Coleman concerning Euler systems for the multiplicative group over arbitrary number fields.

Paraules clau
higher rank Euler systems, multiplicative group, Coleman's conjecture

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Com citar
Burns, David et al. «On Euler systems for the multiplicative group over general number fields». Publicacions Matemàtiques, 2023, vol.VOL 67, núm. 1, p. 89-126, https://raco.cat/index.php/PublicacionsMatematiques/article/view/412622.
Referències
D. Burns and M. Flach, On Galois structure invariants associated to Tate motives, Amer. J. Math. 120(6) (1998), 1343–1397. DOI: 10.1353/ajm.1998.0047

D. Burns and C. Greither, On the equivariant Tamagawa number conjecture for Tate motives, Invent. Math. 153(2) (2003), 303–359

D. Burns, M. Kurihara, and T. Sano, On zeta elements for Gm, Doc. Math. 21 (2016), 555–626.

D. Burns, R. Sakamoto, and T. Sano, On the theory of higher rank Euler, Kolyvagin and Stark systems, IV: the multiplicative group, Preprint (2019). arXiv:1903.09509.

D. Burns and T. Sano, On the theory of higher rank Euler, Kolyvagin and Stark systems, Int. Math. Res. Not. IMRN 2021(13) (2021), 10118–10206. DOI: 10.1093/imrn/rnz103.

D. Burns and S. Seo, On circular distributions and a conjecture of Coleman, Israel J. Math. 241(1) (2021), 343–393. DOI: 10.1007/s11856-021-2098-0.

J. Coates, Elliptic curves with complex multiplication and Iwasawa theory, Bull. London Math. Soc. 23(4) (1991), 321–350. DOI: 10.1112/blms/23.4.321.

R. F. Coleman, On an Archimedian characterization of the circular units, J. Reine Angew. Math. 356 (1985), 161–173. DOI: 10.1515/crll.1985.356.161.

M. Flach, On the cyclotomic main conjecture for the prime 2, J. Reine Angew. Math. 661 (2011), 1–36. DOI: 10.1515/CRELLE.2011.082.

F. F. Knudsen and D. Mumford, The projectivity of the moduli space of stable curves. I: Preliminaries on “det” and “Div”, Math. Scand. 39(1) (1976), 19–55. DOI: 10.7146/math.scand.a-11642.

K. Rubin, A Stark conjecture “over Z” for abelian L-functions with multiple zeros, Ann. Inst. Fourier (Grenoble) 46(1) (1996), 33–62. DOI: 10.5802/aif.1505.

A. Saikia, On units generated by Euler systems, in: “Number Theory and Applications”, Hindustan Book Agency, New Delhi, 2009, pp. 157–174.
DOI: 10.1007/978-93-86279-46-0_12.

T. Sano, Refined abelian Stark conjectures and the equivariant leading term conjecture of Burns, Compos. Math. 150(11) (2014), 1809–1835. DOI: 10.1112/S0010437X14007416.

S. Seo, Circular distributions and Euler systems, J. Number Theory 88(2) (2001), 366–379. DOI: 10.1006/jnth.2000.2634.

S. Seo, Circular distributions and Euler systems, II, Compositio Math. 137(1) (2003), 91–98. DOI: 10.1023/A:1023644822410.

S. Seo, A note on circular distributions, Acta Arith. 114(4) (2004), 313–322. DOI: 10.4064/aa114-4-2.

S. Seo, Circular distributions of finite order, Math. Res. Lett. 13(1) (2006), 1–14. DOI: 10.4310/MRL.2006.v13.n1.a1.

W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62(2) (1980/81), 181–234. DOI: 10.1007/BF01389158.

J. Tate, “Les conjectures de Stark sur les fonctions L d’Artin en s = 0”, Lecture notes edited by Dominique Bernardi and Norbert Schappacher, Progress in Mathematics 47, Birkhäuser Boston, Inc., Boston, MA, 1984.

L. C. Washington, “Introduction to Cyclotomic Fields”, Graduate Texts in Mathematics 83, Springer-Verlag, New York, 1982.
DOI: 10.1007/978-1-4684-0133-2.