A property of ideals of jets of functions vanishing on a set

  • Charles Fefferman

    Princeton University, USA
  • Ary Shaviv

    Princeton University, USA
A property of ideals of jets of functions vanishing on a set cover
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Abstract

For a set that contains the origin, we consider – the set set of all degree Taylor approximations (at the origin) of functions on that vanish on . This set is a proper ideal in – the ring of all degree Taylor approximations of functions on . Which ideals in arise as for some ? In this paper we introduce the notion of a closed ideal in , and prove that any ideal of the form is closed. We do not know whether in general any closed proper ideal is of the form for some , however we prove in a subsequent paper that all closed proper ideals in arise as when .

Cite this article

Charles Fefferman, Ary Shaviv, A property of ideals of jets of functions vanishing on a set. Rev. Mat. Iberoam. (2023), published online first

DOI 10.4171/RMI/1423