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Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces

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How do we study Iwasawa theory?

Iwasawa theory has its origins in the following counterintuitive insight of Iwasawa: instead of trying to describe the structure of any particular Galois module, it is often easier to describe every G …
Hunter Brooks's user avatar
11 votes

Two questions about units in Number Fields

The answer to question 2 as stated is no. Let $K = \mathbb{Q}(\sqrt{p},\sqrt{-b})$, with $p$ 1 mod 4. By Frohlich and Taylor, p. 196, the fundamental unit group is generated by a unit from the real qu …
Hunter Brooks's user avatar