Local Fourier Transforms and Rigidity for D-Modules

By Spencer Bloch, H. Esnault. 2003

80 citations recorded by the source corpus.

Local Fourier trnasforms, analogous to the $\ell$-adic Fourier transforms, are constructed for connections over $k((t))$. Following a program of Katz, a meromorphic connection on a curve is shown to be rigid, i.e. determined by local data at the singularities, if and only if a certain cohomological condition is satisfied. We show that the index of rigidity is invariant under Fourier transform.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bd1fb823bc35d1192983e44e2e60906c6ff5f852

How researchers see this paper

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

In Applied Mathematics

1. Carlos Simpson
2. B. Gross
3. C. Sabbah

In Geometry and Topology

1. B. Gross
2. Carlos Simpson
3. E. Frenkel
4. C. Sabbah
5. Manjul Bhargava
6. T. Arakawa
7. Mark Reeder
8. Haisheng Li

In Mathematical Physics

1. B. Gross
2. Carlos Simpson
3. E. Frenkel
4. C. Sabbah
5. Manjul Bhargava
6. J. Teschner
7. Mark Reeder
8. E. Witten

Citations in the corpus

• Katz's middle convolution algorithm (2006, methodology): “The de Rham version involves replacing local systems by logarithmic connections [113] [13] [72].”
• A rigid irregular connection on the projective line (2009, background): “It also implies that our connection is rigid, in the sense that it has no infinitesimal deformations preserving the formal types at 0 and ∞, as such deformations form an affine space over the first de Rham cohomology group [Katz3, BE ,A].”
• An explicit stationary phase formula for the local formal Fourier-Laplace transform (2007, methodology): “If N∗ denotes HomC((u))(N,C((u))) with its natural connection, we have ρ+(N ∗) ' (ρ+N)∗.”