Introduction To Cyclotomic Fields

By Marina Daecher. 2016

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Explicit Gross–Zagier and Waldspurger formulae (2014, background): “×. For example, if F is a totally real ﬁeld of degree dand Kis a totally imaginary quadratic ﬁeld extension over F, then νb= 21−d· #κb· [O× b : O ×], where κ b⊂ κ1 and #κ1 = 1 or 2 by Theorem 10.3 of [40]. For an inﬁnite place v of F, let Uv denote the maximal compact subgroup of GL2(Fv), which is O”
On fields with the Property (B) (2014, unknown): “It is well-known (see for instance [Wa], p.”
Topological methods in moduli theory (2014, background): “6) is that 2 splits as the direct sum 2 = Rr ⊕ I of a free module with an ideal I ⊂ R, and it is indeed free if the class number h(R) = 1 (to see for which integers m this occurs, see the table in [370], p.”