The Hodge-Arakelov Theory of Elliptic Curves in Positive Characteristic
نویسندگان
چکیده
The purpose of this paper is to study the Hodge-Arakelov theory of elliptic curves (cf. [Mzk1-4]) in positive characteristic. The first two §’s (§1,2) are devoted to studying the relationship of the Frobenius and Verschiebung morphisms of an elliptic curve in positive characteristic to the Hodge-Arakelov theory of elliptic curves. We begin by deriving a “Verschiebung-Theoretic Analogue of the HodgeArakelov Comparison Isomorphism” (Theorem 1.1) which underlies our analysis in §1,2. From this result, we derive, in particular, an explicit description of the étale integral structure of an elliptic curve in positive characteristic (Corollary 1.3). This result may be regarded as a characteristic p version of [Mzk3], Theorem 2.2, which (unlike loc. cit., which holds only for ordinary elliptic curves) is valid even for supersingular elliptic curves.
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