Theta invariants of Euclidean lattices and a question of Quillen
By François Charles
Sphere packings, cyclotomic fields, and subconvexity bounds
By Maryna Viazovska
Appears in collections : Arithmetic geometry, representation theory and applications / Géométrie arithmétique, théorie des représentations et applications, The Fields Medallists, Fields medallists - 1986, Abel Prize
For smooth schemes the category $MF$ (defined by Fontaine for DVR's) realises the "mysterious functor", and provides natural systems of coeffients for crystalline cohomology. We generalise it to schemes with semistable singularities. The new technical features consist mainly of different methods in commutative algebra