TY - JOUR
T1 - On the derived category of Grassmannians in arbitrary characteristic
AU - Buchweitz, Ragnar Olaf
AU - Leuschke, Graham J.
AU - Van Den Bergh, Michel
N1 - Publisher Copyright:
© The Authors 2015.
PY - 2015/7/25
Y1 - 2015/7/25
N2 - In this paper we consider Grassmannians in arbitrary characteristic. Generalizing Kapranov's well-known characteristic-zero results, we construct dual exceptional collections on them (which are, however, not strong) as well as a tilting bundle. We show that this tilting bundle has a quasi-hereditary endomorphism ring and we identify the standard, costandard, projective and simple modules of the latter.
AB - In this paper we consider Grassmannians in arbitrary characteristic. Generalizing Kapranov's well-known characteristic-zero results, we construct dual exceptional collections on them (which are, however, not strong) as well as a tilting bundle. We show that this tilting bundle has a quasi-hereditary endomorphism ring and we identify the standard, costandard, projective and simple modules of the latter.
KW - Grassmannian variety
KW - exceptional collection
KW - quasi-hereditary algebra
KW - semi-orthogonal decomposition
KW - tilting bundle
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U2 - 10.1112/S0010437X14008070
DO - 10.1112/S0010437X14008070
M3 - Article
AN - SCOPUS:84937816187
SN - 0010-437X
VL - 151
SP - 1242
EP - 1264
JO - Compositio Mathematica
JF - Compositio Mathematica
IS - 7
ER -