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Cohomologie des fibr\'es en droites sur SL3 /B en caract\'eristique positive : deux filtrations et cons\'equences
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abstract
In this thesis, I will prove the existence of two filtrations of the cohomology of line bundles on SL_3/B. The first one is a two-step filtration that exists for $H^1(\mu)$ and $H^2(\mu)$ if $\mu$ is in the Griffith region. The second one exists for all $H^i(\mu)$, which is similar to the p-filtration that has been considered by Jens Carsten Jantzen.
Forward citations
Cited by 2 Pith papers
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On the cohomology of line bundles over certain flag schemes
For the intermediate flag scheme D1⊂Hd⊂V over Z, the nonzero cohomology of the line bundle of weight (m,0,...,0,-n-d) is the kernel and cokernel of explicit multinomial coefficient matrices.
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On the cohomology of line bundles over certain flag schemes II
For a prime p and 0 ≤ f ≤ p-2, the top cohomology of the line bundle O(-p-f-d) ⊠ O(p+f) on the incidence variety is the simple GL_{d+1}-module L((p-1+f, p-1, f+1)).
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