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A New Proof Of Cartier'S Third Theorem

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  • Hazewinkel, M.

Abstract

Let Gf A be the category of finite dimensional commutative formal == groups over a ring A. To A one associates a certain, in general noncommutative, ring Cart(A). One then defines a functor G C(G) which assigns to a formal group law G its group of curves which is a module over Cart(A). Theorems 2 and 3 of [1] now say that G C(G) is an equivalence of categories of GfA with a certain full subcategory of Cart(A)-modules. In this paper we give a new proof of theorem 3 of [1], Cartier's third theorem, which asserts that every Cart(A)-module of a certain type comes from a formal group law over A. This proof is based on the constructions of part TV of this series of papers [3].

Suggested Citation

  • Hazewinkel, M., 1978. "A New Proof Of Cartier'S Third Theorem," Econometric Institute Archives 272167, Erasmus University Rotterdam.
    • Handle: RePEc:ags:eureia:272167
    DOI: 10.22004/ag.econ.272167
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