  In this paper, we study the Fitting ideals of Selmer groups over finite
subextensions in the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$ of an
elliptic curve over $\mathbb{Q}$. Especially, we present a proof of the "weak
main conjecture" \`{a} la Mazur and Tate for elliptic curves with good
(supersingular) reduction at an odd prime $p$. We also prove the "strong main
conjecture" suggested by the second named author under the validity of the
$\pm$-main conjecture and the vanishing of a certain error term. The key idea
is the explicit comparison among "finite layer objects", "$\pm$-objects", and
"fine objects" in Iwasawa theory. The case of good ordinary reduction is also
treated.
