A difference ring is a ring with a distinguished endomorphism $\sigma$. Important examples include the ring of holomorphic functions on $\mathbb{C}$ with $\sigma$ taking $f(x)$ to $f(x+1)$, or a ring in positive characteristic $p$ with $\sigma(x) = x^p$. Homomorphisms, ideals, and Weil-stype varieties have natural analogs in this setting. Weil-style difference-algebraic geometry is quite different from the usual algebraic geometry in some ways, is understood rather well via model theory (a branch of mathematical logic), and hasseveral important applications to arithmetic geometry. In proving his celebrated twisted Lang-Weil estimates, Hrushovski needs to do difference-algebaric geometry over rings, including working over $\mathbb{Z}$ to compare the behaviour of the same object in different characteristics. To this end, he sketches out the development of Grothendiek-style difference-algebraic geometry. His first insight is to focus on ``well-mixed'' ideals, a previously overlooked difference version of radical ideals. I will talk about Hrushovski's notion of ``difference schemes'' and some algebraic and model-theoretic notions around it.