Atsuta, Mahiro



Faculty of Science and Technology (Yagami)


Project Assistant Professor (Non-tenured)/Project Research Associate (Non-tenured)/Project Instructor (Non-tenured)


Papers 【 Display / hide

  • Iwasawa theory for class groups of CM fields with p = 2

    Atsuta M.

    Journal of Number Theory (Journal of Number Theory)  204   624 - 660 2019.11

    ISSN  0022314X

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    In this paper, we study Iwasawa theory for p=2. First of all, we show that the classical Iwasawa main conjecture holds true even for p=2 over a totally real field k assuming μ=0 and Leopoldt's conjecture. Using the Iwasawa main conjecture, we study the 2-component of the ideal class group of a CM-field K of finite degree as a Galois module. More precisely, for a CM-field K which is cyclic over the base field k, we determine the Fitting ideal of the minus quotient of the 2-component of the ideal class group. In particular, when k=Q and K/Q is imaginary and cyclic, we prove that the Fitting ideal coincides with the Stickelberger ideal.

  • Finite Λ-submodules of iwasawa modules for a CM-field for p = 2

    Atsuta M.

    Journal de Theorie des Nombres de Bordeaux (Journal de Theorie des Nombres de Bordeaux)  30 ( 3 ) 1017 - 1035 2018

    ISSN  12467405

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    Let p be a prime, X F− the minus quotient of the IWasaWa module, Which We define to be the Galois ∞ group of the maximal unramified abelian pro-p-extension over the cyclotomic Z p -extension over a CM field F. If p is an odd prime, it is Well knoWn that X F−∞ has no non-trivial finite Z p [[Gal(F ∞ /F)]]-submodule. But X F− has non-trivial finite Z p [[Gal(F ∞ /F)]]-submodule in some cases for p = 2. ∞ In this paper, We study the maximal finite Z p [[Gal(F ∞ /F)]]-submodule of X F−∞ for p = 2. We determine the size of the maximal finite Z 2 [[Gal(F ∞ /F)]]-submodule of X F− ∞ under some mild assumptions.

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