Number/Representation Theory

The classical Dieudonne theory classifies $p$-divisible groups over a perfect field $k$ in terms of semi-linear algebra over $W(k)$. In this talk, I will explain a conjectural generalization - due to Drinfeld - of Dieudonne's classification to a broader class of rings, whose spectra form a basis for the fpqc topology on $p$-nilpotent schemes. A key input in Drinfeld's approach is a certain square-zero extension of the ring of Witt vectors, known as the ring of sheared Witt vectors.