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Higher Fitting Ideals of Iwasawa Modules


The work of Iwasawa, beginning with a seminal paper in 1958 [7], provided a

fruitful method of studying the structure of ideal class groups and other algebraic objects by viewing them inside of a p-adic tower of fields and then considering the corresponding object at the top of the tower as a module over a topological ring now called an Iwasawa algebra. One way to analyze the structure of these modules over the appropriate ring is to determine the Fitting ideals of the module; however, in the literature thus far only the initial Fitting ideal has been the object of close study. In this dissertation, we prove a conjecture by Kurihara about the higher Fitting ideals of Iwasawa modules of certain abelian number fields. This result shows that they are in essence generated by the special values of L-functions arising from a family of extensions of the number field.

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