Canonical coordinates on the canonical lift
英文摘要:
In this article we prove the existence of a canonical theta structure for the canonical lift of an ordinary abelian variety.
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Robert Carls
In this article we prove the existence of a canonical theta structure for the canonical lift of an ordinary abelian variety.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
继续探索
In this note, we prove a finiteness result for fibers that are canonical lifts in a given elliptic fibration. The question was motivated by the authors' construction of an arithmetic Euler top, and it highlights an interesting discrepancy between the arithmetic and the classical case: in the former, it is impossible to extend the flows to a compactification of the phase space, viewed as an elliptic fibration over the space of action variables.
In this article we give a Galois-theoretic characterization of the canonical theta structure. The Galois property of the canonical theta structure translates into certain $p$-adic theta relations which are satisfied by the canonical theta null point of the canonical lift. As an application we give a purely algebraic proof of some 2-adic theta identities which describe the set of theta null points of the canonical lifts of ordinary abelian varieties in characteristic 2. The latter theta relations are suitable for explicit canonical lifting.
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