RATIONAL POINTS OF QUIVER MODULI SPACES

For a perfect base field k, we investigate arithmetic aspects of moduli spaces of quiver representations over k: we study actions of the absolute Galois group of k on the (k) over bar -valued points of moduli spaces of quiver representations over k and we provide a modular interpretation of the fixed-point set using quiver representations over division algebras, which we reinterpret using moduli spaces of twisted quiver representations (we show that those spaces provide different k-forms of the initial moduli space of quiver representations). Finally, we obtain that stable (k) over bar -representations of a quiver are definable over a certain central division algebra over their field of moduli.