{"id":"openai-math/A-Conditional-Reduction-for-Algebraic-Kuga-Satake-Correspondences","pdf":"https://github.com/openai/math/blob/main/preprints/A-Conditional-Reduction-for-Algebraic-Kuga-Satake-Correspondences-September-10-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Conditional-Reduction-for-Algebraic-Kuga-Satake-Correspondences-September-10-2026","tags":["algebraic-geometry","k3-surfaces","hodge-theory"],"score":0,"title":"A Conditional Reduction for Algebraic Kuga–Satake Correspondences","domain":"Algebraic and complex geometry","family":"032","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"For a polarized K3 surface whose primitive cohomology has full orthogonal Hodge group, one algebraic correspondence inducing a nonzero map from that cohomology to the second cohomology of an abelian variety suffices to recover the prescribed full Kuga–Satake correspondence. We give an equivalent condition using holomorphic one-forms on a generically finite surface cover. If this input holds very generally in a polarized component, the prescribed correspondence is algebraic throughout that component, for every choice of standard data on the transcendental part. The existence of the initial…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-10","reactions":{},"formalized":false,"family_title":"The rational Hodge conjecture for CM abelian varieties"}