Abstract: Motivated by Dieudonné theory, V. Drinfeld and E. Lau introduced a "decompletion" of the ring of Witt vectors W(R) of a derived p-complete ring R such that (R/p)_{red} is perfect, extending a construction of T. Zink. I will explain various characterizations of this decompletion (called the sheared Witt vectors) and some examples. I will also explain two applications: a conjectural description of p-divisible groups over such rings (due to Drinfeld and Lau), and a decompletion of the stack of prismatization. (Joint work in progress with Bhargav Bhatt, Vadim Vologodsky, and Mingjia Zhang, and partially also with Artem Kanaev.)