{"paper":{"title":"The algebraic formalism of soliton equations over arbitrary base fields","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"A. \\'Alvarez V\\'azquez, F. J. Plaza Mart\\'in, J. M. Mu\\~noz Porras","submitted_at":"1996-06-10T18:09:23Z","abstract_excerpt":"The aim of this paper is to offer an algebraic construction of infinite-dimensional Grassmannians and determinant bundles (and therefore valid for arbitrary base fields). As an application we construct the $\\tau$-function and formal Baker-Akhiezer functions over arbitrary fields, by proving the existence of a ``formal geometry'' of local curves analogous to the geometry of global algebraic curves.\n  We begin by defining the functor of points, $\\fu{\\gr}(V,V^+)$, of the Grassmannian of a $k$-vector space $V$ in such a way that its rational points are precisely the points of the Grassmannian defi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9606009","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}