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Number Theory Seminar
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
2010/06/02
16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Ryoko Tomiyasu (KEK)
On some algebraic properties of CM-types of CM-fields and their
reflex fields (JAPANESE)
Ryoko Tomiyasu (KEK)
On some algebraic properties of CM-types of CM-fields and their
reflex fields (JAPANESE)
[ Abstract ]
Shimura and Taniyama proved in their theory of complex
multiplication that the moduli of abelian varieties of a CM-type and their
torsion points generate an abelian extension, not of the field of complex
multiplication, but of a reflex field of the field. In this talk, I
introduce some algebraic properties of CM-types, half norm maps that might
shed new light on reflex fields.
For a CM-field $K$ and its Galois closure $K^c$ over the rational field $Q$,
there is a canonical embedding of $Gal (K^c/Q)$ into $(Z/2Z)^n \\rtimes S_n$.
Using properties of the embedding, a set of CM-types $\\Phi$ of $K$ and their
dual CM-types $(K, \\Phi)$ is equipped with a combinatorial structure. This
makes it much easier to handle a whole set of CM-types than an individual
CM-type.
I present a theorem that shows the combinatorial structure of the dual
CM-types is isomorphic to that of a Pfister form.
Shimura and Taniyama proved in their theory of complex
multiplication that the moduli of abelian varieties of a CM-type and their
torsion points generate an abelian extension, not of the field of complex
multiplication, but of a reflex field of the field. In this talk, I
introduce some algebraic properties of CM-types, half norm maps that might
shed new light on reflex fields.
For a CM-field $K$ and its Galois closure $K^c$ over the rational field $Q$,
there is a canonical embedding of $Gal (K^c/Q)$ into $(Z/2Z)^n \\rtimes S_n$.
Using properties of the embedding, a set of CM-types $\\Phi$ of $K$ and their
dual CM-types $(K, \\Phi)$ is equipped with a combinatorial structure. This
makes it much easier to handle a whole set of CM-types than an individual
CM-type.
I present a theorem that shows the combinatorial structure of the dual
CM-types is isomorphic to that of a Pfister form.
