Title: Class invariants for Quartic CM fields

Abstract: One can define class invariants for a quartic primitive CM field K as special values of certain Siegel (or Hilbert) modular functions at CM points corresponding to K. Such constructions were given in De Shalit-Goren's generalization of elliptic units and in Igusa's modular invariants associated to genus 2 curves. We provide explicit bounds on the primes appearing in the denominators of these algebraic numbers. This allows us, in particular, to construct S-units in certain abelian extensions of K, where S is effectively determined by K, and to bound primes of bad reduction for genus 2 curves with CM. This talk will also highlight the relationship with the work of Bruinier and Yang. This is joint work with Eyal Goren.