Franco-Asian Summer School on Arithmetic Geometry

Explore advanced topics in arithmetic geometry through this comprehensive summer school featuring 23 lectures from leading researchers in the field. Delve into cutting-edge developments including upper ramification groups of local fields with imperfect residue fields, prismatic cohomology, p-adic Simpson correspondence, and syntomic cohomology. Examine the intricate connections between algebraic geometry and number theory through detailed presentations on L-functions for unitary groups, modularity over CM fields, and Galois representations over p-adic varieties. Study specialized topics such as automatic de Rhamness of p-adic local systems, duality for p-adic pro-étale cohomology of analytic curves, and Sen theory for locally analytic representations. Investigate geometric aspects including graded logarithmic geometry, valuative spaces, Hodge standard conjectures, and parallel transport for Higgs bundles over p-adic curves. Learn about local epsilon factors of vanishing cycles, Sen operators and Lie algebras from Galois representations, and bounding techniques for perverse sheaves in characteristic p, providing a comprehensive foundation in modern arithmetic geometry research.

Syllabus

Takeshi Saito - Upper ramification groups of local fields with imperfect residue fields (1/3)
Takeshi Saito - Upper ramification groups of local fields with imperfect residue fields (2/3)
Alexander Petrov - Automatic de Rhamness of p-adic local systems and Galois action on the (...)
Takeshi Tsuji - Prismatic cohomology and A_inf-cohomology with coefficients
Wiesława Nizioł - Duality for p-adic pro-étale cohomology of analytic curves
Ahmed Abbes - The p-adic Simpson correspondence: Functoriality by proper direct image and (...) 1/3
Ahmed Abbes - The p-adic Simpson correspondence: Functoriality by proper direct image and (...) 2/3
Takeshi Saito - Upper ramification groups of local fields with imperfect residue fields (3/3)
Daichi Takeuchi - On local epsilon factors of the vanishing cycles of isolated singularities
Quentin Guignard - Graded logarithmic geometry and valuative spaces
Yifeng Liu - Derivative of L-functions for unitary groups (1/3)
Yifeng Liu - Derivative of L-functions for unitary groups (2/3)
Ahmed Abbes - The p-adic Simpson correspondence: Functoriality by proper direct image and (...)
Yifeng Liu - Derivative of L-functions for unitary groups (3/3)
Teruhisa Koshikawa - Some cases of the Hodge standard conjecture
Ana Caraiani - Modularity over CM fields
Akhil Mathew - Some recent advances in syntomic cohomology (1/3)
Akhil Mathew - Some recent advances in syntomic cohomology (2/3)
Lue Pan - Sen theory for locally analytic representations
Tongmu He - Sen operators and Lie algebras arising from Galois representations over p-adic varieties
Daxin Xu - Parallel transport for Higgs bundles over p-adic curves
Akhil Mathew - Some recent advances in syntomic cohomology (3/3)
Will Sawin - Bounding the stalks of perverse sheaves in characteristic p via the (...)