扭曲的德利涅模与有限域上的阿贝尔簇

中文摘要 AI 辅助

有限域上阿贝尔簇的同源类由Tate和Honda描述。Deligne证明有限域上普通阿贝尔簇的范畴等价于普通Deligne模的范畴。Centeleghe和Stix将Deligne的结果推广到整个阿贝尔簇范畴，但当基有限域非素时，目标范畴与Deligne模无关。本文引入广义和扭曲Deligne模，给出Deligne定理更直接的推广。

英文摘要

Isogeny classes of abelian varieties over finite fields were described by Tate and Honda. Deligne proved that the category of ordinary abelian varieties over a finite field is equivalent to the category of ordinary Deligne modules. Centeleghe and Stix extended Deligne's results to the whole category of abelian varieties, but, if the base finite field is not prime, then the target category is not related to Deligne modules. In this paper we introduce generalized and twisted Deligne modules and give a more direct generalization of the Deligne theorem.

发表机构

• Ben-Gurion University of the Negev（内盖夫本-古里安大学）

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