The Eisenstein cocycle and Gross's tower of fields conjecture

Dasgupta S, Spieß M (2016)
Annales mathématiques du Québec 40(2): 355-376.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor/in
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Abstract / Bemerkung
This paper is an announcement of the following result, whose proof will be forthcoming. Let F be a totally real number field, and let be a tower of fields with L / F a finite abelian extension. Let I denote the kernel of the natural projection from to . Let denote the Stickelberger element encoding the special values at zero of the partial zeta functions of L / F, taken relative to sets S and T in the usual way. Let r denote the number of places in S that split completely in K. We show that , unless K is totally real in which case we obtain and . This proves a conjecture of Gross up to the factor of 2 in the case that K is totally real and . In this article we sketch the proof in the case that K is totally complex.
Stichworte
Stickelberger elements; Eisenstein cocycle; Gross's conjecture
Erscheinungsjahr
2016
Zeitschriftentitel
Annales mathématiques du Québec
Band
40
Ausgabe
2
Seite(n)
355-376
ISSN
2195-4755
eISSN
2195-4763
Page URI
https://pub.uni-bielefeld.de/record/2905506

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Dasgupta S, Spieß M. The Eisenstein cocycle and Gross's tower of fields conjecture. Annales mathématiques du Québec. 2016;40(2):355-376.
Dasgupta, S., & Spieß, M. (2016). The Eisenstein cocycle and Gross's tower of fields conjecture. Annales mathématiques du Québec, 40(2), 355-376. doi:10.1007/s40316-015-0046-2
Dasgupta, S., and Spieß, M. (2016). The Eisenstein cocycle and Gross's tower of fields conjecture. Annales mathématiques du Québec 40, 355-376.
Dasgupta, S., & Spieß, M., 2016. The Eisenstein cocycle and Gross's tower of fields conjecture. Annales mathématiques du Québec, 40(2), p 355-376.
S. Dasgupta and M. Spieß, “The Eisenstein cocycle and Gross's tower of fields conjecture”, Annales mathématiques du Québec, vol. 40, 2016, pp. 355-376.
Dasgupta, S., Spieß, M.: The Eisenstein cocycle and Gross's tower of fields conjecture. Annales mathématiques du Québec. 40, 355-376 (2016).
Dasgupta, Samit, and Spieß, Michael. “The Eisenstein cocycle and Gross's tower of fields conjecture”. Annales mathématiques du Québec 40.2 (2016): 355-376.