2025/07/09 by Arkhipov, Sergei I., Mikhail V. Bondarko, Bondarko, Mikhail V.
Mathematics · #18F20 #55R25 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #K-Theory and Homology (math.KT) #Primary 14F20 14G17 #secondary 14M10 19F27 16E10 13B40
paper · pdf · doi:10.48550/arxiv.2507.06816
openalex publication_date 2025/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish new general etale versions of theorems of Barth and Sommese. Respectively, we compute the lower etale cohomology of closed subvarieties of PN of small codimensions and of their preimages with respect to proper morphisms (that are not necessarily finite; this statement is completely new), and also of the zero loci of sections of ample vector bundles; all these statements are valid over fields of arbitrary characteristics. To obtain these results, we use a new 'fat hyperplane section' Weak Lefschetz-type theorem for etale cohomology of non-projective varieties that is related to a result of Goresky and MacPherson (over complex numbers).