Cluster algebras with coefficients and relative Calabi-Yau structures
By Bernhard Keller
Categorified Crystal Bases on Localized Quantum Coordinate Rings and Cellular Crystals
By Toshiki Nakashima
Appears in collection : Conférence de mi-parcours du programme ANRThéorie de Hodge p-adique et Développements (ThéHopaD)
This is a joint work with Colmez and Dospinescu. We show that the reduction modulo p of an absolutely irreducible p-adic Bach space representation of $GL_2(Q_p)$ has the shape predicted by the mod p Langlands correspondence. The result had been known for p>3 previously, the new proof works for all primes p.