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The algebraic formalism of soliton equations over arbitrary base fields. (English) Zbl 0995.14021
Rodríguez, Rubí (ed.) et al., Workshop on abelian varieties and theta functions. Morelia, México, July 8-27, 1996. Proceedings. México: Sociedad Matemática Mexicana. Aportaciones Mat., Investig. 13, 3-40 (1998).
This interesting paper offers an algebraic construction of infinite-dimensional Grassmannians and determinant bundles. The authors also construct $$\tau$$-functions and formal Baker-Akhiezer functions over arbitrary fields. They prove the existence of a “formal geometry” of local curves analogous to the geometry of global algebraic curves. The treatment is not like Segal-Wilson theory, but the formalism might clarify aspects of conformal field theories over base fields other than $$\mathbb{R}$$ or $$\mathbb{C}$$.
For the entire collection see [Zbl 0948.00031].

##### MSC:
 14M15 Grassmannians, Schubert varieties, flag manifolds 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials