Mixed characteristic 
means that a local ring 
has ring
characteristic 0 while its residue field has
field characteristic 
. Since the residue is a field,
is a prime number. For example, the localization 
has ring
characteristic 0 and residue field 
. This differs from equal characteristic, in which the ring characteristic of the local
ring equals the field characteristic
of its residue field. Mixed characteristic is one
of the distinctions in the Gersten conjecture
and in Serre's intersection multiplicity
(Weibel 2013).
Mixed Characteristic
See also
Field Characteristic, Gersten Conjecture, Local Ring, Residue Field, Ring Characteristic, Serre's Intersection MultiplicityExplore with Wolfram|Alpha
References
Weibel, C. A. The K-Book: An Introduction to Algebraic K-Theory. Providence, RI: Amer. Math. Soc., 2013. https://sites.math.rutgers.edu/~weibel/Kbook.html.Cite this as:
Weisstein, Eric W. "Mixed Characteristic." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MixedCharacteristic.html