Drinfeld Moduli Schemes and Infinite Grassmannians

Abstract

The aim of this paper is to construct an immersion of the Drinfeld moduli schemes in a finite product of infinite Grassmannians, such that they will be locally closed subschemes of these Grassmannians which represent a kind of flag varieties. This construction is derived from two results: the first is that the moduli functor of vector bundles with an ∞-formal level structure (defined below) over a curve X is representable, in a natural way, by a closed subscheme of the infinite Grassmannian. The second is an equivalence (see [8], [19], [7], [6], [6]) between Drinfeld A-modules of rank n and elliptic sheaves, extended for level structures in [?]. Let us detail these results. Let X be a smooth, proper and geometrically irreducible curve over a finite field Fq, ∞ a rational point ofX , A = H (X−∞,OX), D an effective divisor over Spec(A), and S an arbitrary scheme over Fq. Â ∞ denotes the ring of adeles outside ∞ and

Cite this paper

@inproceedings{Alvarez1997DrinfeldMS, title={Drinfeld Moduli Schemes and Infinite Grassmannians}, author={Amelia Alvarez}, year={1997} }