D-Modules and Microlocal Calculus

By Masaki Kashiwara. 2002

251 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/937f7192ff33973bfc88af26d08a3a1196a84ac1

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Citations in the corpus

Chern-Simons theory and S-duality (2011, background): “4.1 Simple S-dualities 47 4.2 A-polynomial and amoebas 49 4.3 Dual loop coordinates 50 4.4 Dual D-modules 51”
Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions (2007, unknown): “[55, 56]), namely the operator P = −λx∂x − μ.”
A-polynomial, B-model, and quantization (2011, background): “There is also a mathematical theory of D-modules [7–9], which studies modules over rings of differential operators, and in particular operators with properties analogous to those which we expect from Â.”
Derived equivalence for quantum symplectic resolutions (2011, background): “7 of [Ka1] for more details in the setting of microdifferential operators.”
F-thresholds and Bernstein–Sato Polynomials (2004, methodology): “Moreover, bf,0 has simple roots −(5) 6 ,−1,−(7) 6 (see [Ka1], Example 6.”
Stacks of quantization-deformation modules on complex symplectic manifolds (2003, unknown): “In Section 5 we overview the theory of Sato-Kawai-Kashiwara [17] of microdifferential operators and modules over such rings (see also [18], [11] for a detailed exposition).”
Wild Harmonic Bundles and Wild Pure Twistor D-modules (2008, background): “1 of [47], we obtain the following standard proposition.”
Derived Categories (2016, background): “Algebraic analysis, including differential, microdifferential and DQ modules (see [74], [134], [77]) and microlocal sheaf theory (see [75]), with its application to symplectic topology (see [149], [110]).”
The Character Theory of a Complex Group (2009, methodology): “The seminal works of Harish Chandra, Kashiwara, Kazhdan, Lusztig, Beilinson, Bernstein and other early pioneers place D-modules at the heart of representation theory.”
Symmetries and stabilization for sheaves of vanishing cycles (2012, background): “(6.13) Observe that the work of Behrend–Fantechi and Kashiwara–Schapira cited above supports the existence of (6.12)–(6.13): there are natural products ExtkOS (K 1/2 L ,K 1/2 M )⊗OS Ext l OS (K 1/2 M ,K 1/2 N ) −→ Ext k+l OS (K 1/2 L ,K 1/2 N ), RH om(D•, E•) L ⊗RH om(E•,F•) −→ RH om(D•,F•).”