Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor D-Modules

By T. Mochizuki. 2003

187 citations recorded by the source corpus.

Part 4. An Application to the theory of Pure Twistor $D$-modules: Pure twistor $D$-module Prolongation of $\mathcal R$-module $\mathcal E$ The filtrations of $\mathfrak{E} [\eth_t]$ The weight filtration on $\psi_{t,u}\mathfrak{E}$ and the induced $\mathcal{R}$-triple The sesqui-linear pairings Polarized pure twistor $D$-module and tame harmonic bundles The pure twistor $D$-modules on a smooth curve (Appendix) Part 5. Characterization of Semisimplicity by Tame Pure Imaginary Pluri-harmonic Metric: Preliminary Tame pure imaginary harmonic bundle The Dirichlet problem in the punctured disc case Control of the energy of twisted maps on a Kahler surface The existence of tame pure imaginary pluri-harmonic metric Bibliography Index.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/31247a4ebd02b1bb186436b164122ef96bca6705

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

On the classification of rank-two representations of quasiprojective fundamental groups (2007, background): “tem with quasi-unipotent monodromy at inﬁnity. If V is rigid as deﬁned in §6 then it underlies a complex variation of Hodge structure of weight one. Proof: This is Corollary 1 of [28], see also [59], [85]. Since we are talking about rank two local systems, there are two possibilities for the Hodge t”
Mixed Twistor D-modules (2011, methodology): “The following proposition is essentially proved in [35], based on the results in the Hodge case in [5], [6], [7] and [24].”
Hodge theoretic aspects of mirror symmetry (2008, unknown): “Sim97b] and T.Mochizuki [Moc06a, Moc06b, Moc07a , Moc07b] under the names of”
Wild Harmonic Bundles and Wild Pure Twistor D-modules (2008, methodology): “77 in [67]), we can show that there exist a large number N > 0 and a finite subset S ⊂ R×C with the following property: • u∈S ( s+λ−1e(λ, u) )N · IC(m,σ∗μ)(s) is naturally extended to the continuous function on I(λ0)×T (−R), which is holomorphic with respect to s.”
Local Systems on Proper Algebraic V -manifolds (2010, background): “Our discussion of nonabelian harmonic theory on stacks adds to a subject which has already been treated by several authors [12] [36] [45] [103], and for the case of root stacks it is closely related to harmonic theory for parabolic bundles [15] [29] [64] [74] [70] [71] [84] [100].”
Unit Interval Orders and the Dot Action on the Cohomology of Regular Semisimple Hessenberg Varieties (2015, unknown): “to use the Kashiwara conjecture for semisimple perverse sheaves [26], which has been proved by T. Mochizuki and independently by combining work of A.J. de Jong, Drinfeld, Gaitsgory, and B¨ockle–Khare [32, 33, 10, 14, 16, 6]. This allows us to point out strong forms of Theorems 54 and Theorem 57. See”
Kobayashi-Hitchin correspondence for tame harmonic bundles II (2006, methodology): “See also Mochizuki [15].”
The Hodge theory of algebraic maps (2003, background): “2] has recently extended M. Saito’s results to the case of semisimple local systems on X by developing his own theory of polarizable twistor D-modules. See also the related work by T. Mochizuki [20], [21]. While Saito’s results cover and pre-date some of the results of this paper, namely the Relativ”
Katz's middle convolution algorithm (2006, background): “It would be good to have the full middle-convolution theory for the general setup of parabolic logarithmic λ-connections [110] [111] [112] [125].”