Speakers: Lei Fu (Nankai University), Byungheup Jun (ASARC, KAIST), Dong Uk Lee (KIAS), Myung Sung (Inha University)

 

Date: 2008.5.22.(Thu), 2:00 PM -- 5.24 (Sat)

 

Aim of the workshop: We present a gentle introduction and survey on some of the topics of the list below. We begin with the construction of derived category, then construct the Riemann-Hilbert correspondences in complex analytic, l-adic, and p-adic setting. Related topics and some recent results will be presented. This is a crash course on the subject aimed at Graduate students and researchers working in arithmetic geometry, algebraic geometry and number theory.

 

 

Topics:

Myung Sung

: Derived category, t-structure, Perverse sheaf I

Myung Sung

: Derived category, t-structure, Perverse sheaf II

Lei Fu

: etale sheaf, l-adic sheaf, derived category of l-adic sheaf, 6 operations on the derived category,
perverse t-structure, Verdier duality I

Lei Fu

: etale sheaf, l-adic sheaf, derived category of l-adic sheaf, 6 operations on the derived category,
perverse t-structure, Verdier duality II

Lei Fu

: etale sheaf, l-adic sheaf, derived category of l-adic sheaf, 6 operations on the derived category,
perverse t-structure, Verdier duality III

Lei Fu

: etale sheaf, l-adic sheaf, derived category of l-adic sheaf, 6 operations on the derived category,
perverse t-structure, Verdier duality IV

Lei Fu

: etale sheaf, l-adic sheaf, derived category of l-adic sheaf, 6 operations on the derived category,
perverse t-structure, Verdier duality V

Lei Fu

: etale sheaf, l-adic sheaf, derived category of l-adic sheaf, 6 operations on the derived category,
perverse t-structure, Verdier duality VI

Byungheup Jun

: monodromy and local systems, regular holonomic D-modules,
Riemann-Hilbert correspondence, Fourier transformation I

Byungheup Jun

: monodromy and local systems, regular holonomic D-modules,
Riemann-Hilbert correspondence, Fourier transformation II

Byungheup Jun

: monodromy and local systems, regular holonomic D-modules,
Riemann-Hilbert correspondence, Fourier transformation III

Byungheup Jun

: monodromy and local systems, regular holonomic D-modules,
Riemann-Hilbert correspondence, Fourier transformation IV

Byungheup Jun

: monodromy and local systems, regular holonomic D-modules,
Riemann-Hilbert correspondence, Fourier transformation V

Byungheup Jun

: monodromy and local systems, regular holonomic D-modules,
Riemann-Hilbert correspondence, Fourier transformation VI

Dong Uk Lee

: p-adic monodromy and Riemann-Hilbert correspondence I

Dong Uk Lee

: p-adic monodromy and Riemann-Hilbert correspondence II

Dong Uk Lee

: p-adic monodromy and Riemann-Hilbert correspondence III

Dong Uk Lee

: p-adic monodromy and Riemann-Hilbert correspondence IV

 

 

References:

1. A. Borel et al.: Algebraic D-modules. Perspectives in Mathematics,

2. Academic Press (1987) 2. A. Beilinson, J. Bernstein, P. Deligne: Faisceaux pervers. Analysis and topology on singular spaces, I (Luminy, 1981), 5--171, Asterisque, 100. SMF, 1982

3. G. Laumon: Transformation de Fourier, constantes d'equations fonctionnelles et conjecture de Weil. IHES Publ. Math. No. 65 (1987), 131--210

4. R. Kiehl, R. Weissauer: Weil conjectures, perverse sheaves and l-adic Fourier transform. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., 42. Springer-Verlag

5. N. Katz: Rigid local systems, Ann. of Math. Studies, 139. Princeton University Press (1996)

6. M. Emerton, M. Kisin: An introduction to the Riemann-Hilbert correspondence for uni F-crystals -- Geometric aspects of Dwork theory II, 677-700 (2004)

 

Contacts:

Byungheup Jun (byungheup(at)gmail(dot)com)

Dong Uk Lee (dulee(at)kias(dot)re(dot)kr)