Finiteness of endomorphism algebras of CM modular abelian varieties | Zendy

Josep González | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Finiteness of endomorphism algebras of CM modular abelian varieties

Author(s) -

Josep González

Publication year - 2011

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/651

Subject(s) - endomorphism , abelian group , modular design , mathematics , pure mathematics , algebra over a field , computer science , programming language

Let Af be the abelian variety attached by Shimura to a normalized newform f ∈ S2(Γ1(N)). We prove that for any integer n > 1 the set of pairs of endomorphism algebras ( EndQ(Af )⊗Q,EndQ(Af )⊗Q ) obtained from all normalized newforms f with complex multiplication such that dimAf = n is finite. We determine that this set has exactly 83 pairs for the particular case n = 2 and show all of them. We also discuss a conjecture related to the finiteness of the set of number fields EndQ(Af ) ⊗ Q for the non-CM case.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research