A 
-typical Witt vector over a commutative
ring 
, for a fixed prime number 
, is a sequence 
with addition and multiplication specified by
universal integer polynomials through the ghost
components
 |
The operations make every ghost component a ring homomorphism. They are defined by these universal polynomials
even when the ghost map is not injective in 
.
For a perfect field 
of field characteristic 
, the Witt vector ring 
is a complete discrete
valuation ring of ring characteristic
zero, with residue field 
and uniformizer 
(Milne 2017, p. 228). For example, 
.
The integral form of Donovan's conjecture uses
as its fixed coefficient ring (Eaton et al. 2020, p. 249).
