ABSTRACT: Let F, G, and H be relatively prime forms in two variables over a field of finite characteristic p. The module of relations between these forms is free on two homogeneous generators, and the "syzygy gap" is defined to be the difference between the degrees of the generators. I'm interested in studying the syzygy gaps for varying powers of three fixed forms. Raising the forms to the p-th power multiplies the syzygy gap by p; this leads to the construction of a function with remarkable self-similarity properties. Applications to Hilbert - Kunz functions will be given; these supply further evidence that Hilbert - Kunz theory is related to "dynamical systems in characteristic p".
 
 

For further information visit the Seminar web site at http://mystic.math.neu.edu/alexmart/rtrt.html  or contact Alex Martsinkovsky <alexmart@neu.edu>