It is a well-known fact that holomorphic functions extend across subsets of
codimension 2. Restricting to the subclass of Siegel modular forms, the Koecher
principle states that these functions even extend holomorphically across the
1-codimensional boundary of a (toroidal) compactication of the underlying
Siegel modular variety provided its complex dimension is greater than 1. As a
direct consequence of this principle, Siegel modular forms possess a convergent
Fourier{Jacobi expansion. Surprisingly, it turns out that also the converse holds,
i. e., a formal Fourier{Jacobi expansion gives rise to a Siegel modular form and is
thus automatically convergent. We will report about a cohomological approach
to the solution of this conjecture by Steve Kudla.