منابع مشابه
Examples of abelian surfaces with everywhere good reduction
We describe several explicit examples of simple abelian surfaces over real quadratic fields with real multiplication and everywhere good reduction. These examples provide evidence for the Eichler–Shimura conjecture for Hilbert modular forms over a real quadratic field. Several of the examples also support a conjecture of Brumer and Kramer on abelian varieties associated to Siegel modular forms ...
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Given an elliptic curve E1 over a number field K and an element s in its 2-Selmer group, we give two different ways to construct infinitely many Abelian surfaces A such that the homogeneous space representing s occurs as a fibre of A over another elliptic curve E2. We show that by comparing the 2Selmer groups of E1, E2 and A, we can obtain information about X(E1/K)[2] and we give examples where...
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For a complex abelian surface A with endomorphism ring isomorphic to the maximal order in a quartic CM-field K, the Igusa invariants j1(A), j2(A), j3(A) generate an unramified abelian extension of the reflex field of K. In this paper we give an explicit geometric description of the Galois action of the class group of this reflex field on j1(A), j2(A), j3(A). Our description can be expressed by ...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2017
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s179304211750052x