Generalized theta functions, Drinfeld modules and some arithmetic consequences
Let \(C\) be a smooth, proper and geometrically irreducible curve defined over a finite field \(\mathbb{F}_q\). In the paper under review, the author determines Plücker coordinates for rank-\(n\) Drinfeld modules. The coordinates are obtained by means of the values that certain theta functions take over the module, these theta functions being defined as sections of the generalized theta divisor (as defined by \textit{J.-M. Drezet} and \textit{M. S. Narasimhan} [Invent. Math. 97, No. 1, 53--94 (1989; Zbl 0689.14012)]) on the moduli space of vector bundles over \(C\). After determining the coordinates the author proceeds to use some of the results obtained to establish an algebraic-geometric Riemann theorem for the generalized theta divisor.
scientific article; zbMATH DE number 2153783
scientific article