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An arithmetic algebraic regularity lemma (joint with Atticus Stonestrom)

Tao proved an "algebraic regularity lemma" about graphs definable with bounded complexity in finite fields (partly as a tool for results about expanding polynomials). We give an "arithmetic" version, namely with pairs (G,A) of a group and subset, in place of bipartite graphs. We compare to Green's arithmetic regularity lemma for vector spaces over finite fields, as well as discussing stronger versions for simply connected semisimple algebraic groups over finite fields.