JournalsjemsVol. 20, No. 11pp. 2643–2683

Partial zeta values, Gross's tower of fields conjecture, and Gross–Stark units

  • Samit Dasgupta

    University of California at Santa Cruz, USA

  • Michael Spieß

    Universität Bielefeld, Germany
Partial zeta values, Gross's tower of fields conjecture, and Gross–Stark units cover
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Abstract

We prove a conjecture of Gross regarding the “order of vanishing” of Stickelberger elements relative to an abelian tower of fields and give a cohomological construction of the conjectural Gross–Stark units. This is achieved by introducing an integral version of the Eisenstein cocycle.

Cite this article

Samit Dasgupta, Michael Spieß, Partial zeta values, Gross's tower of fields conjecture, and Gross–Stark units. J. Eur. Math. Soc. 20 (2018), no. 11, pp. 2643–2683

DOI 10.4171/JEMS/821