Adelic Extension Classes, Atiyah Bundles and Non-Commutative Codes

Original · EN

This paper consists of three components. In the first, we give an adelic interpretation of the classical extension class associated to extension of locally free sheaves on curves. Then, in the second, we use this construction on adelic extension classes to write down explicitly adelic representors in GLᵣ(A) for Atiyah bundles Iᵣ on elliptic curves. All these works make sense over any base fields. Finally, as an application, for m≥ 1, we construct the global sections of Iᵣ(mQ) in local terms and apply it to obtain rank r MDS codes based on the codes spaces CF;ᵣ(D; Iᵣ(mQ)) introduced in our earlier paper [Codes and Stability].