Multiplicity in difference geometry

21 February 2013
Ivan Tomasic
The study of difference algebraic geometry stems from the efforts of Macintyre and Hrushovski to count the number of solutions to difference polynomial equations over fields with powers of Frobenius. We propose a notion of multiplicity in the context of difference algebraic schemes and prove a first principle of preservation of multiplicity. We shall also discuss how to formulate a suitable intersection theory of difference schemes.