zbMATH — the first resource for mathematics

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].

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