  We formulate an Iwasawa main conjecture for a higher rank Euler system for a
general motive. We prove "one half" of the main conjecture under mild
hypotheses. We also formulate a conjecture on "Darmon-type derivatives" of
Euler systems and give an application to the Tamagawa number conjecture.
Lastly, we specialize our general framework to the setting of Heegner points
and give a natural interpretation of the Heegner point main conjecture in terms
of rank two Euler systems.

Number Theory