The Eisenstein cocycle, partial zeta values and Gross--Stark units
  We introduce an integral version of the Eisenstein cocycle. As applications 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. 
Samit Dasgupta, Michael Spie{\ss}
math.NT