论文标题
通过增强的Ind-Sheves中等生长和附近循环的快速衰减
Moderate Growth and Rapid Decay Nearby Cycles via Enhanced Ind-Sheaves
论文作者
论文摘要
对于复杂的歧管$ x $，对于任何全体形函数$ f \ colon x \ to \ mathbb {c} $，我们定义和研究与$ x $增强的Ind-Sheaf相关的中等增长和快速衰减对象。这些将是沿$ f $的$ x $的真实面向爆破空间。我们表明，在d'Agnolo-kashiwara的不规则Riemann-hilbert对应关系的背景下，这些对象恢复了经典的De Rham复合物，其中等增长和与全体$ \ MATHCAL {D} _X _X _X _X $ -MODULE相关的快速衰减。 为了证明后者，我们解决了这些自动含量$ \ Mathcal {d} _x $模块的近期猜想双重性，通过与正常的交叉分裂的增长条件，通过与kashiwara-schapira的经典双重性结果在某些台接量学上的空间之间取得了经典的双重性能，从而沿着正常的交叉除数界生长。通过标准的诉讼论点，我们证明了Sabbah对任意除数的猜想。作为推论，我们恢复了代数de rham的共同体学和与Bloch-Esnault和Hien引起的平滑品种上的可集成连接相关的快速衰减同源之间众所周知的完美配对。
For any holomorphic function $f\colon X\to \mathbb{C}$ on a complex manifold $X$, we define and study moderate growth and rapid decay objects associated to an enhanced ind-sheaf on $X$. These will be sheaves on the real oriented blow-up space of $X$ along $f$. We show that, in the context of the irregular Riemann--Hilbert correspondence of D'Agnolo--Kashiwara, these objects recover the classical de Rham complexes with moderate growth and rapid decay associated to a holonomic $\mathcal{D}_X$-module. In order to prove the latter, we resolve a recent conjectural duality of Sabbah between these de Rham complexes of holonomic $\mathcal{D}_X$-modules with growth conditions along a normal crossing divisor by making the connection with a classic duality result of Kashiwara--Schapira between certain topological vector spaces. Via a standard dévissage argument, we then prove Sabbah's conjecture for arbitrary divisors. As a corollary, we then recover the well-known perfect pairing between the algebraic de Rham cohomology and rapid decay homology associated to integrable connections on smooth varieties due to Bloch--Esnault and Hien.
