Wild Harmonic Bundles and Wild Pure Twistor D-modules

By T. Mochizuki. 2008

219 citations recorded by the source corpus.

We study (i) asymptotic behaviour of wild harmonic bundles, (ii) the relation between semisimple meromorphic flat connections and wild harmonic bundles, (iii) the relation between wild harmonic bundles and polarized wild pure twistor $D$-modules. As an application, we show the hard Lefschetz theorem for algebraic semisimple holonomic $D$-modules, conjectured by M. Kashiwara.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ba376d8c772184c863bcced4ac8665a21234a78f

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Periods for flat algebraic connections (2008, background): “ an asymptotic one on small multisectors. In dimension two, this is the ingredient of [23], II.2, in higher dimensions it can be derived from Mochizuki’s approach of good lattices and can be found in [20] also, see the remark after the theorem below. Let Ad Xe|Z denote the formal completion of AXe a”
Asymptotic behaviour of certain families of harmonic bundles on Riemann surfaces (2015, methodology): “We note that we can obtain these estimates in an elementary way which is standard in the study of the asymptotic behaviour of harmonic bundles around the singularity, pioneered by Simpson [20], and pursued further by the author [13, 16].”
Good formal structure for meromorphic flat connections on smooth projective surfaces (2008, background): “In [ 17 ], the author intends to establish the correspondence of semisimple algebraic holonomic D-modules and polarizable wild pure twistor”
Kobayashi-Hitchin correspondence for tame harmonic bundles II (2006, background): “n k, it is called a regular λ-ﬂat c-parabolic bundle in codimension k. Remark 2.1 We often omit to state “regular” in this paper, because we always assume regularity. Non-regular case is discussed in [32]. Let E∗ = E,{cE} c ∈ RS be a ﬁltered sheaf on (X,D). A regular λ-connection of E∗ is a λ-connec”
Good formal structures for flat meromorphic connections, I: Surfaces (2008, result): “However, if both f ∗E and f ∗ End(E) have good formal structures in the sense of Sabbah, then f ∗E has a good formal structure in the sense of Mochizuki.”