Math @ Duke

Publications [#338509] of Samit Dasgupta
Papers Published
 Dasgupta, S; Spieß, M, The Eisenstein cocycle and Gross’s tower of fields conjecture,
Annales Mathématiques Du Québec, vol. 40 no. 2
(August, 2016),
pp. 355376, Springer Nature [doi]
(last updated on 2019/05/19)
Abstract: © 2016, Fondation CarlHerz and Springer International Publishing Switzerland. This paper is an announcement of the following result, whose proof will be forthcoming. Let F be a totally real number field, and let F⊂ K⊂ L be a tower of fields with L / F a finite abelian extension. Let I denote the kernel of the natural projection from Z[ Gal (L/ F) ] to Z[ Gal (K/ F) ]. Let Θ ∈ Z[ Gal (L/ F) ] 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 Θ ∈ Ir, unless K is totally real in which case we obtain Θ ∈ Ir1 and 2 Θ ∈ Ir. This proves a conjecture of Gross up to the factor of 2 in the case that K is totally real and # S≠ r. In this article we sketch the proof in the case that K is totally complex.


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