q-bic forms

A q-bic form is a pairing $V\times V\to k$ that is linear in the second variable and q-power Frobenius linear in the first; here, V is a vector space over a field k containing the finite field $F_{q^2}$. This article develops a geometric theory of q-bic forms in the spirit of that of bilinear forms. I find two filtrations intrinsically attached to a q-bic form, with which I define a series of numerical invariants. These are used to classify, study automorphism group schemes of, and describe specialization relations in the parameter space of q-bic forms.