  We develop a detailed arithmetic theory related to special values at
arbitrary integers of the Artin $L$-series of linear characters. To do so we
define canonical generalized Stark elements of arbitrary `rank' and `weight',
thereby extending the classical theory of Rubin-Stark elements. We then
formulate an extension to arbitrary weight of the refined version of the
Rubin-Stark Conjecture that we studied in an earlier article and also show that
generalized Stark elements constitute a $p$-adic family by formulating precise
conjectural congruence relations between elements of differing weights. We
prove both of these conjectures in several important cases.
