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beilinsonWindow -- extract the subquotient complex which contributes to the Beilinson window

Synopsis

• Usage:
W=beilinsonWindow T
• Inputs:
• T, , a (part of a) Tate resolution on a product of t projective spaces
• Outputs:
• W, ,

Description

Extract the terms which under the U-functor defined in Tate Resolutions on Products of Projective Spaces contributed to the Beilinson complex U(T) of T, i.e. W is the smallest free subquotient complex of T such that U(W) = U(T)

 i1 : n={1,1}; i2 : (S,E) = productOfProjectiveSpaces n; i3 : W=(chainComplex {map(E^0,E^1,0),map(E^1,E^0,0)})[1] 1 o3 = 0 <-- E <-- 0 -1 0 1 o3 : ChainComplex i4 : time T=tateExtension W; -- used 0.60695s (cpu); 0.310037s (thread); 0s (gc) i5 : cohomologyMatrix(T,-{3,3},{3,3}) o5 = | 8h 4h 0 4 8 12 16 | | 6h 3h 0 3 6 9 12 | | 4h 2h 0 2 4 6 8 | | 2h h 0 1 2 3 4 | | 0 0 0 0 0 0 0 | | 2h2 h2 0 h 2h 3h 4h | | 4h2 2h2 0 2h 4h 6h 8h | 7 7 o5 : Matrix (ZZ[h, k]) <-- (ZZ[h, k]) i6 : W=beilinsonWindow T 1 o6 = 0 <-- E <-- 0 -1 0 1 o6 : ChainComplex i7 : cohomologyMatrix(W,-{2,2},{2,2}) o7 = | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 1 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | 5 5 o7 : Matrix (ZZ[h, k]) <-- (ZZ[h, k]) i8 : a={2,-3} o8 = {2, -3} o8 : List i9 : W2=beilinsonWindow (T**E^{a}[sum a]) 4 11 6 o9 = E <-- E <-- E -1 0 1 o9 : ChainComplex i10 : cohomologyMatrix(W2,-{2,2},{2,2}) o10 = | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 8h 4h 0 0 | | 0 6h 3h 0 0 | | 0 0 0 0 0 | 5 5 o10 : Matrix (ZZ[h, k]) <-- (ZZ[h, k]) i11 : cohomologyMatrix(tateExtension W2,-{2,2},{2,2}) o11 = | 18h 12h 6h 0 6 | | 15h 10h 5h 0 5 | | 12h 8h 4h 0 4 | | 9h 6h 3h 0 3 | | 6h 4h 2h 0 2 | 5 5 o11 : Matrix (ZZ[h, k]) <-- (ZZ[h, k])