Geometric structure of ends of Ricci shrinkers

We study blow-up sequences of Ricci shrinkers without global curvature assumptions based at points q at which the scalar curvature satisfies a Type I bound, proving that their F-limits split a line. In the four-dimensional case these limits are smooth Ricci shrinkers and the convergence is in the pointed smooth Cheeger-Gromov sense. As a consequence, limits along the integral curve of grad(f) starting at such a point q split a line. This generalises known results about the geometry of ends of Ricci shrinkers that relied on global curvature bounds. To obtain our results, we extend the F-convergence theory from R. Bamler and Yu Li and Bing Wang.