Some results in Iwasawa Theory and the p-adic representation theory of p-adic GL₂
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This thesis is divided into two parts. In the first, we generalize results of Greenberg-Vatsal on the behavior of algebraic lambda-invariants of p-ordinary modular forms under congruence. In the second, we generalize a result of Emerton on maps between locally algebraic parabolically induced representations and unitary Banach space representations of GL₂ over a p-adic field.