Rennes, from May 12th to May 23rd, 2014
Contact: C. Mourougane
Scientific board: X. Caruso, F. Charles, M. Gros, C. Mourougane

We organize a spring school on complex and p-adic aspects of the Hodge theory with a view towards deformation theory.

The first week is devoted to constructions of complex and p-adic Hodge theories, for a single smooth variety or for a smooth family of smooth varieties. In the complex setting, construction of moduli spaces thanks to Torelli type theorems will be the main target. In the p-adic setting, the first aim will be the constructions of cohomological tools and the second aim the statement and the proof in a special case of comparison theorems between p-adic cohomologies.

Hodge theories of deformations with singular fibers will be the topic of the second week. In the complex setting, one leading theme will be the use of Hodge theory in the description of properties of moduli spaces like hyperbolicity. Similarly, some properties of étale cohomologies and more surprisingly complex cohomologies will be derived from p-adic Hodge theory.

Each course will be given in English and divided into three lectures of 90 minutes.