Igor Krichever introduced an algebro-geometric construction of solutions of KP equations starting from an algebraic curve with some additional data.


George Wilson introduced the [adelic Grassmannian](https://mathoverflow.net/questions/338024/explanation-of-definition-of-george-wilsons-adelic-grassmannian), which is a subspace of the Sato Grassmannian parametrizing all solutions to KP equations. 


Question: can every point of Wilson's adelic Grassmannian be obtained by Krichever's algebro-geometric construction?



Can every point of Wilson's adelic Grassmannian be obtained by Krichever construction of solutions to KP equations?
Yes - the adelic Grassmannian precisely parametrizes "rational solutions of KP", which are the Krichever solutions attached to rank 1 torsion free sheaves on cuspidal genus 0 curves -- i.e. curves with $P^1$ as their bijective normalization (or subrings of the field of rational functions). Its adelic (or factorization) nature is explained by keeping track of the finite subset of $P^1$ which is the location of the cusps - i.e. this space parametrizes "Hecke modifications" (Backlund transformations) supported at given points of $P^1$. This is stated as Corollary 5.21 in <https://arxiv.org/abs/math/0212094> though I think was known to Wilson, Berest, Mulase and others. 


