  Using a temperature-dependent potential obtained from lattice gauge
calculations, we study the stability of heavy quarkonia in the quark-gluon
plasma. We find that only the Upsilon(1S) and the eta_b(1S) are bound in the
quark-gluon plasma, and have a small binding energy. The quark-gluon plasma may
be revealed by an Upsilon(1S) dilepton peak with an invariant mass close to
twice the current b quark mass, which is lower than the Upsilon(1S) mass in
free space. The quarkonia Upsilon(1S) and eta_b(1S) can dissociate by collision
with quarks and gluons in the quark-gluon plasma. We evaluate the dissociation
cross section of the Upsilon(1S) due to gluon absorption. The Upsilon(1S) and
the eta_b(1S) can also dissociate spontaneously at temperatures above the
dissociation temperature 1.11T_c, where T_c is the quark-gluon plasma phase
transition temperature. At temperatures slightly above the dissociation
temperature these states appear as resonances, which provides another signature
for the quark-gluon plasma.
