coApproximationSequence -- Short exact sequence of the MCM coapproximation

Usage:

E = coApproximationSequence M
Inputs:
- M, a module,
Outputs:
- E, a complex,

Description

The coapproximation sequence of a module M over a Gorenstein ring is the versal short exact sequence $$0\to M \to P \to M' \to 0$$ where M' is a maximal Cohen-Macaulay module and P is a module of finite projective dimension, as defined by Auslander and Buchweitz.

i1 : S = ZZ/101[a,b]/ideal(a^3+b^3)

o1 = S

o1 : QuotientRing

i2 : R = S/ideal(a*b)

o2 = R

o2 : QuotientRing

i3 : M = R^1/(ideal vars R)^2

o3 = cokernel | a2 0 b2 |

                            1
o3 : R-module, quotient of R

i4 : coApproximationSequence M

                                2
o4 = cokernel {-2} | -b2 | <-- R  <-- M
              {-2} | -a2 |             
                               2      3
     1

o4 : Complex

For the programmer

The object coApproximationSequence is a function closure.

The source of this document is in MCMApproximations.m2:620:0.

coApproximationSequence -- Short exact sequence of the MCM coapproximation

Description

See also

For the programmer