We study the S-arithmetic (co)homology of reductive groups over number
fields with coefficients in (duals of) certain locally algebraic and locally
analytic representations for finite sets of primes S. We use our results to
construct eigenvarieties associated to parabolic subgroups at places in S and
certain classes of supercuspidal and algebraic representations of their Levi
factors. We show that these agree with eigenvarieties constructed using
overconvergent homology and that for definite unitary groups they are closely
related to the Bernstein eigenvarieties constructed by Breuil-Ding.Comment: 85 pages. Comments are welcom