Summer school "p-adic cohomologies and arithmetic applications" is organized by the Mathematical Research Institute of the University of Sevilla (IMUS) and will take place at the Faculty of Mathematics on June 14-18, 2010.



Bernard Le Stum:  "Introduction to rigid cohomology"

Lecture 1. Sheaves and cohomology.
Lecture 2. Ultrametric geometry.
Lecture 3. Rigid cohomology. | Lecture notes |
Lecture 4. Crystalline interpretation.
Lecture 5. Independance theorems.
Lecture 6. Properties and applications.

Nobuo Tsuzuki:  "Overconvergent F-isocrystals and rigid cohomology on curves"

Lecture 1. Rigid cohomology and overconvergent F-isocrystals.
Lecture 2. Crew's conjecture.
Lecture 3. Unit-root cases.
Lecture 4. Kedlaya's filtration.
Lecture 5. Application of Crew's conjecture.

Steven Sperber: "Dwork cohomology and applications"

Lecture 1. Dwork's trace formula, the Dwork complex, dual complex and applications (degree, p-divisiblity).
Lecture 2. Cohomology, L-functions of non-degenerate toric exponential sums.
Lecture 3. Zeta functions of   complete intersections (toric, projective cases).
Lecture 4. Families of varieties and exponential sums, p-adic differential equation, unit-root formulas, L-functions of symmetric powers.

Douglas Haessig: "An introduction to Dwork's p-adic analytic representation of an additive character"

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