Holmstrom Special values II

arXiv:1209.5018 The $p$-adic Shintani cocycle from arXiv Front: math.NT by G. Ander Steele The Shintani cocycle on $\GL_n(\Q)$, as constructed by Hill, gives a cohomological interpretation of special values of zeta functions for totally real fields of degree $n$. We give an explicit criterion for a specialization of the Shintani cocycle to be $p$-adically interpolable. As a corollary, we recover the results of Deligne-Ribet, Cassou Noguès and Barsky on the construction of $p$-adic $L$-functions attached to totally real fields.

arXiv:1210.7460 Addendum to: Milne, Values of zeta functions of varieties over finite fields, Amer. J. Math. 108, (1986), 297-360 fra arXiv Front: math.AG av J. S. Milne The original article expressed the special values of the zeta function of a variety over a finite field in terms of the $\hat{Z}$-cohomology of the variety. As the article was being completed, Lichtenbaum conjectured the existence of certain motivic cohomology groups. Progress on his conjecture allows one to give a beautiful restatement of the main theorem of the article in terms of $Z$-cohomology groups.

nLab page on Special values II