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Universität Augsburg
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Universität Augsburg
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Alexander Samokhin
Universität Düsseldorf
spricht am
Dienstag, 2. Mai 2017
um
15:45 Uhr
im
Raum 1005 (L1)
über das Thema:
| Abstract: |
| Given a semi-simple algebraic group G and its Borel subgroup B ⊂ G over a perfect field of characteristic p>0, and a line bundle on the flag variety G/B, we consider the direct image of such a line bundle under the Frobenius morphism on G/B. One expects that this latter vector bundle decomposes into a direct sum of indecomposable vector bundles with multiplicities, while each indecomposable summand is defined over the integers and is independent of the characteristic. Knowing indecomposable summands of these direct images for line bundles corresponding to p–restricted weights may clarify, in particular, cohomology vanishing patterns of line bundles on G/B in characteristic p. We are going to explain an approach to calculating these Frobenius direct images that is based on semi-orthogonal decompositions in derived categories. As an example, we are going to show the so-called Andersen–Haboush identity, which immediately implies Kempf's vanishing theorem. |
| Hierzu ergeht herzliche Einladung. |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).