Description of the seminar
The seminar aims to understand the model theory of the field of Witt vectors over an infinite perfect field when endowed with the canonical lift of the Frobenius, the Witt-Frobenius. We will first go through the classical relative quantifier elimination for henselian valued fields in equicharacteristic zero, deducing the Ax-Kochen/Ershov theorem for both equicharacteristic zero and unramified mixed characteristic. We will then prove analogous theorems for isometric valued difference fields in equicharacteristic zero, deducing the Ax-Kochen/Ershov theorem for both equicharacteristic zero and unramified mixed characteristic (i.e., the Witt-Frobenius).
