There is an emerging field of arithmetic algebraic geometry whose objects of study are varieties, often not finite-dimensional, equipped with commuting families of lifts of Frobenius maps. Important roles are played by schemes of Witt vectors, arithmetic jet spaces, and the spectra of lambda-rings. In a certain precise sense, these varieties make up an absolute algebraic geometry, lying over a deeper base than the ring of integers.
The workshop will be centered around the following partly introductory lecture series, each of 3-5 hours.
Pierre Cartier: Lambda-rings and Witt vectors
Lars Hesselholt: The de Rham-Witt complex
Alexandru Buium: Arithmetic differential equations
James Borger: Lambda-algebraic geometry
The workshop has two main purposes. The first is to introduce beginning and established researchers to this new field. The second is to provide an opportunity for experts to discuss applications to other parts of arithmetic algebraic geometry, such as function fields, the field with one element, explicit class field theory, and realizations of motives. We encourage workers in all fields of number theory and arithmetic algebraic geometry to attend.