  We introduce the study of frames and equiangular lines in classical
geometries over finite fields. After developing the basic theory, we give
several examples and demonstrate finite field analogs of equiangular tight
frames (ETFs) produced by modular difference sets, and by translation and
modulation operators. Using the latter, we prove that Gerzon's bound is
attained in each unitary geometry of dimension $d = 2^{2l+1}$ over the field
$\mathbb{F}_{3^2}$. We also investigate interactions between complex ETFs and
those in finite unitary geometries, and we show that every complex ETF implies
the existence of ETFs with the same size over infinitely many finite fields.
