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HYBRID RESEARCH SCHOOL – ÉCOLE DE RECHERCHE

Franco-Asian Summer School on Arithmetic Geometry in Luminy
École d’été franco-asiatique sur la géométrie arithmétique à Luminy

30 May – 3 June 2022

Scientific Committee
Comité scientifique

Ahmed Abbes (CNRS – IHES)
Ana Caraiani (Imperial College London)
Takeshi Saito (The University of Tokyo)
Takeshi Tsuji (The University of Tokyo)
Organizing Committee
Comité d’organisation

Ahmed Abbes (CNRS – IHES)
Ariane Mézard (Sorbonne Université)
Takeshi Saito (The University of Tokyo)
Weizhe Zheng (Chinese Academy of Sciences)
Description
This summer school is a continuation of the many fruitful joint France-Asia events that have taken place since the Asian Year on Motives initiated by J.-M. Fontaine at IHES in 2006. These collaborations have had a considerable impact on the international development of fundamental branches of arithmetic geometry. This new event, organized at CIRM, will be open to students and young researchers from all over the world. It will consist in four mini-courses and several lectures on the most recent advances in four fundamental fields:

– p-adic Hodge theory,
– Ramification of étale l-adic sheaves and epsilon factors,
– Homotopical algebra techniques and applications to motives;
– Geometric aspects of Shimura varieties
Cette école d’été s’inscrit dans la continuation des nombreux et fructueux événements conjoints France-Asie ayant eu lieu depuis la Asian Year on Motives initiée par J.-M. Fontaine à l’IHÉS en 2006. Ces collaborations ont eu un impact considérable sur le développement international de branches fondamentales de la géométrie arithmétique. Ce nouvel événement, organisé au CIRM, sera ouvert aux étudiantes et étudiants et jeunes chercheuses et chercheurs du monde entier. Il consistera en quatre mini-cours ainsi que de nombreux exposés sur les avancées les plus récentes dans quatre domaines fondamentaux :

– la théorie de Hodge p-adique,
– la ramification des faisceaux étale l-adique et les facteurs epsilon,
– les techniques d’algèbre homotopique et leurs applications aux motifs,
– les aspects géométriques des variétés de Shimura.

Speakers

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Courses (3 hours each)

Ahmed Abbes (CNRS & IHÉS)    The p-adic Simpson correspondence: Functoriality by proper direct image and Hodge-Tate local systems   
Yifeng Liu (Institute of Advanced Study in Mathematics, Zhejiang University)    Derivative of L-functions for unitary groups
Akhil Mathew (University of Chicago)    Some recent advances in syntomic cohomology
Takeshi Saito (University of Tokyo)    Upper ramification groups of local fields with imperfect residue fields

Lectures (1 hour each)

Ana Caraiani (Imperial College London)    Modularity over CM fields
Quentin Guignard (Université de Paris)    Graded logarithmic geometry and valuative spaces
Tongmu He (IHES & Université Paris-Saclay)    Sen operators and Lie algebras arising from Galois representations over p-adic varieties
Teruhisa Koshikawa (RIMS)    Some cases of the Hodge standard conjecture
Wieslawa Niziol (CNRS & Sorbonne Université)    Duality for p-adic pro-étale cohomology of analytic curves
Lue Pan (Princeton University)    Sen theory for locally analytic representations
Alexander Petrov (Harvard)    Automatic de Rhamness of p-adic local systems and Galois action on the pro-algebraic fundamental group
Will Sawin (Columbia University)    Bounding the stalks of perverse sheaves in characteristic p via the characteristic cycle
Daichi Takeuchi (Riken)    On local epsilon factors of the vanishing cycles of isolated singularities
Takeshi Tsuji (The University of Tokyo)    Prismatic cohomology and A_inf-cohomology with coefficients
Daxin Xu (Chinese Academy of Sciences)    Parallel transport for Higgs bundles over p-adic curves

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