Abstract: The comparison isomorphism in p-adic Hodge theory asserts that
in some sense, the p-adic etale cohomology and the algebraic de Rham cohomology
of a smooth proper variety over a finite extension of Q_p determine each
other. We propose an alternate interpretation in which the central
object is a standard auxiliary object in p-adic Hodge theory called a
(phi, Gamma)-module, from which p-adic etale cohomology and algebraic de
Rham cohomology are functorially derived using mechanisms introduced by
Fontaine. The hope is to then enrich this object to carry additional
structures especially for varieties defined over number fields; we
illustrate this by showing how to incorporate the rational structure of
de Rham cohomology. (This depends on joint work with Chris Davis.)