亚纯联络与Gauss和的Epantic因子
Epsilon Factors for Meromorphic Connections and Gauss Sums
摘要：
设$E$是某个域$k \subset \cplx$在$\proj^1/k$上具有亚纯联络的向量丛，$\mathbf{E}$是$X$的解析点上的水平截面层.不规则的黎曼-希尔伯特对应指出，$L$的De Rham上同调与$\mathbf{L}$的“适度增长”上同调之间存在典范同构。Beilinson、Bloch和Esnault最近的工作表明，这个映射的行列式分解成局部“$ε$ -因子”的乘积，这与伽罗瓦表示的经典$ε$ -因子非常相似。在本文中，我们表明，$ε$ -因素秩1连接可以明确计算的高斯和。这个公式暗示了德拉姆$ε$因子和伽罗瓦因子之间更深层次的关系。
英文摘要：
Let $E$ is be vector bundle with meromorphic connection on $\proj^1/k$ for some field $k \subset \cplx$, and let $\mathbf{E}$ 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 $\mathbf{L}$. 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.
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