Presented By: Student Commutative Algebra Seminar - Department of Mathematics
Student CA Seminar - Cohen Structure Theorem
Havi Ellers
The Cohen Structure Theorem classifies all Noetherian
complete local rings as quotients of power series rings. The statement is most
concise in equicharacteristic, but can be stated in mixed characteristic as well,
and in both cases the proof hinges on the existence of a “coefficient ring”. In
this talk we introduce coefficient rings, discuss their existence, and then
state the Cohen Structure theorem in both equi- and mixed characteristics.
complete local rings as quotients of power series rings. The statement is most
concise in equicharacteristic, but can be stated in mixed characteristic as well,
and in both cases the proof hinges on the existence of a “coefficient ring”. In
this talk we introduce coefficient rings, discuss their existence, and then
state the Cohen Structure theorem in both equi- and mixed characteristics.
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