2010/10/12 by Christopher L. Bremer, Bremer, Christopher L.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1010.2272
openalex publication_date 2010/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let E is be vector bundle with meromorphic connection on \proj1/k for some field k ⊂ \cplx, and let E be the sheaf of horizontal sections on the analytic points of X. The irregular Riemann-Hilbert correspondence states that there is a canonical isomorphism between the De Rham cohomology of L and the `moderate growth' cohomology of L. Recent work of Beilinson, Bloch, and Esnault has shown that the determinant of this map factors into a product of local `ε-factors' which closely resemble the classical ε-factors of Galois representations. In this paper, we show that ε-factors for rank one connections may be calculated explicitly by a Gauss sum. This formula suggests a deeper relationship between the De Rham ε-factor and its Galois counterpart.