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This is a continuation of our study of the foundations of D-branes from theviewpoint of Grothendieck in the region of the related Wilson's theory-spacewhere "branes" are still branes. In this work, we focus on D-strings andconstruct the moduli stack of morphisms from Azumaya prestable curves $C^{Az}$with a fundamental module ${\cal E}$ to a fixed target $Y$ of a givencombinatorial type. Such a morphism gives a prototype for a Wick-rotatedD-string of B-type on $Y$, following the Polchinski-Grothendieck Ansatz, andthis stack serves as a ground toward a mathematical theory of topologicalD-string world-sheet instantons.

Morphisms from Azumaya prestable curves with a fundamental module to a projective variety: Topological D-strings as a master object for curves