2024/11/26 by Shiquan Li, Li, Shiquan
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.2411.17410
openalex publication_date 2024/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let S be a noetherian normal scheme, and let X→ S be a surjective projective morphism of pure relative dimension d. We construct a symmetric multi-additive functor Pic(X)d+1 → Pic(S), and prove its functorial properties. Our construction uses Elkik's and García's ideas, as well as algebraic Hartogs' theorem. Moreover, our results can be used to define arithmetic intersection theory of hermitian line bundles for equidimensional morphisms.