Good formal structure for meromorphic flat connections on smooth projective surfaces
By T. Mochizuki. 2008
73 citations recorded by the source corpus.
We prove the algebraic version of a conjecture of C. Sabbah on the existence of the good formal structure for meromorphic flat connections on surfaces after some blow up.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/d577c7e8fdf12a517c97a3bf4ead7fc8bc7a94b0
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In Applied Mathematics
- Kiran S. Kedlaya
- C. Sabbah
- M. Hien
- T. Mochizuki
- A. D'agnolo
- Masaki Kashiwara
- Kentaro Nakamura
- Ruochuan Liu
In Geometry and Topology
- Kiran S. Kedlaya
- C. Sabbah
- T. Mochizuki
- M. Hien
- Masaki Kashiwara
- A. D'agnolo
- Carlos Simpson
- D. Hernandez
Citations in the corpus
- Good formal structures for flat meromorphic connections, I: Surfaces (2008, background): “This does not permit the sort of reduction modulo p arguments used in [25].”
- Mixed Twistor D-modules (2011, background): “44 and resolution of turning points ([27], [28], see also [37] and [38]), we obtain the existence of a dual of T .”
- Periods for flat algebraic connections (2008, background): “Lately, a proof of Sabbah’s Conjecture in the case of algebraic connections (which lie in the main focus of our work) has been achieved by T. Mochizuki (see [ 16 ]).”
- Introduction to Stokes Structures (2009, background): “Kedlaya [38] (when dimX = 2, one refers to [37]; in the algebraic setting and dimX = 2, one can use [60], and [65] for dimX > 3, see Remark 11.”
- Good formal structures for flat meromorphic connections, II: Excellent schemes (2010, methodology): “The methods of [34] and [26] are quite different; Mochizuki uses reduction to positive characteristic and some study of pcurvatures, whereas we use properties of differential modules over one-dimensional nonarchimedean analytic spaces.”
- The Stokes Structure of a good meromorphic flat bundle (2011, background): “In [19] and [21], we have established it in the algebraic case.”
- Riemann-Hilbert correspondence for holonomic D-modules (2013, result): “According to the results of Mochizuki [22, 23] and Kedlaya [19, 20] (see §7.”