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• W2893256505 abstract "Let $mathcal{A}$ be an abelian variety over a number field, with a good reduction at a prime ideal containing a prime number $p$. Denote by ${rm A}$ an abelian variety over a finite field of characteristic $p$, obtained by the reduction of $mathcal{A}$ at the prime ideal. In this paper we derive an algorithm which allows to decompose the group scheme ${rm A}[p]$ into indecomposable quasi-polarized ${rm BT}_1$-group schemes. This can be done for the unramified $p$ on the basis of its decomposition into prime ideals in the endomorphism algebra of ${rm A}$. We also compute all types of such correspondence for abelian varieties of dimension up to $5$. As a consequence we establish the relation between the decompositions of prime $p$ and the corresponding pairs of $p$-rank and $a$-number of an abelian variety ${rm A}$." @default.
• W2893256505 created "2018-10-05" @default.
• W2893256505 creator A5011905327 @default.
• W2893256505 creator A5066749398 @default.
• W2893256505 date "2018-09-27" @default.
• W2893256505 modified "2023-09-27" @default.
• W2893256505 title "Computing algorithm for reduction type of CM abelian varieties." @default.
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