Epsilon Factors for Meromorphic Connections and Gauss Sums

الأصل · EN

Let E is be vector bundle with meromorphic connection on ¹/k for some field k ⊂, 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.