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Given an odd prime number $p$ and a $p$-stabilized Artin representation$\rho$ over $\mathbb{Q}$, we introduce a family of $p$-adic Stark regulatorsand we formulate an Iwasawa-Greenberg main conjecture and a $p$-adic Starkconjecture which can be seen as an explicit strengthening of conjectures byPerrin-Riou and Benois in the context of Artin motives. We show that theseconjectures imply the $p$-part of the Tamagawa number conjecture for Artinmotives at $s=0$ and we obtain unconditional results on the torsionness ofSelmer groups. We also relate our new conjectures with various main conjecturesand variants of $p$-adic Stark conjectures that appear in the literature. Inthe case of monomial representations, we prove that our conjectures areessentially equivalent to some newly introduced Iwasawa-theoretic conjecturesfor Rubin-Stark elements. We derive from this a $p$-adic Beilinson-Starkformula for finite-order characters of an imaginary quadratic field in which$p$ is inert.  Along the way, we prove that the Gross-Kuz'min conjecture unconditionallyholds for abelian extensions of imaginary quadratic fields.

On generalized Iwasawa main conjectures and $p$-adic Stark conjectures for Artin motives