Rational points of quiver moduli spaces

Abstract

For a perfect field $k$, we study actions of the absolute Galois group of $k$ on the $\bar{k}$-valued points of moduli spaces of quiver representations over $k$; the fixed locus is the set of $k$-rational points and we obtain a decomposition of this fixed locus indexed by elements in the Brauer group of $k$. We provide a modular interpretation of this decomposition using quiver representations over division algebras, and we reinterpret this description using twisted quiver representations. We also see that moduli spaces of twisted quiver representations give different forms of the moduli space of quiver representations.