We compute the strand of T as defined in Tate Resolutions on Products of Projective Spaces Theorem 0.4. If T is (part of) the Tate resolution of a sheaf F, then the I-strand of T through c correponds to the Tate resolution RπJ*(F(c)) where J ={0,...,t-1}- I is the complement and πJ: ℙP →∏j ∈J ℙnj denotes the projection.
i1 : n={1,1};(S,E)=setupRings(ZZ/101,n);
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i3 : T1 = (dual res trim (ideal vars E)^2)[1]; |
i4 : a=-{2,2};T2=T1**E^{a}[sum a];
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i6 : W=beilinsonWindow T2,cohomologyTable(W,-2*n,2*n)
15 16 4
o6 = (0 <-- 0 <-- E <-- E <-- E <-- 0, | 0 0 0 0 0 |)
| 0 0 0 0 0 |
-2 -1 0 1 2 3 | 0 8 15 0 0 |
| 0 4 8 0 0 |
| 0 0 0 0 0 |
o6 : Sequence
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i7 : T=sloppyTateExtension W; |
i8 : cohomologyTable(T,-{3,3},{3,3})
o8 = | 12h 4 20 36 52 68 84 |
| 10h 3 16 29 42 55 68 |
| 8h 2 12 22 32 42 52 |
| 6h 1 8 15 22 29 36 |
| 4h 0 4 8 12 16 20 |
| 2h h 0 1 2 3 4 |
| 0 2h 4h 6h 8h 10h 12h |
7 7
o8 : Matrix (ZZ[h, k]) <--- (ZZ[h, k])
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i9 : sT1=strand(T,-{1,1},{1});
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i10 : cohomologyTable(sT1,-{3,3},{3,3})
o10 = | 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 4h 0 4 8 12 16 20 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
7 7
o10 : Matrix (ZZ[h, k]) <--- (ZZ[h, k])
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i11 : sT2=strand(T,{1,1},{0});
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i12 : cohomologyTable(sT2,-{3,3},{3,3})
o12 = | 0 0 0 0 52 0 0 |
| 0 0 0 0 42 0 0 |
| 0 0 0 0 32 0 0 |
| 0 0 0 0 22 0 0 |
| 0 0 0 0 12 0 0 |
| 0 0 0 0 2 0 0 |
| 0 0 0 0 8h 0 0 |
7 7
o12 : Matrix (ZZ[h, k]) <--- (ZZ[h, k])
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i13 : sT3=removeZeroTrailingTerms strand(T,{1,-1},{0,1})
12
o13 = 0 <-- E <-- 0
-1 0 1
o13 : ChainComplex
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i14 : cohomologyTable(sT3,-{3,3},{3,3})
o14 = | 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 12 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
7 7
o14 : Matrix (ZZ[h, k]) <--- (ZZ[h, k])
|