Arithmetic of the oscillator representation
This unfinished manuscript of 1987 uses Mumford's theory of theta functions to construct the bundle of Siegel modular forms of weight 1/2 algebraically, along with the action of Hecke operators and of certain homogeneous differential operators. Since the oscillator representation is naturally defined over the maximal abelian extension of Q, one needs to replace the Siegel modular variety by a certain infinite cover (parametrizing additive characters) to obtain a theory rational over Q. It was intended to include proofs of a q-expansion principle in weight 1/2 and a study of the rationality of the theta correspondence for dual reductive pairs when one of the factors is compact at the real place, but the corresponding sections were never written. The article in its unfinished state may still be of some interest.
The transfer to tex introduced numerous typographical errors, many of which undoubtedly remain.