| Softcover ISBN: | 978-2-37905-216-3 |
| Product Code: | PASY/64 |
| List Price: | $119.00 |
| AMS Member Price: | $95.20 |
| Softcover ISBN: | 978-2-37905-216-3 |
| Product Code: | PASY/64 |
| List Price: | $119.00 |
| AMS Member Price: | $95.20 |
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Book DetailsPanoramas et SynthèsesVolume: 64; 2025; 347 ppMSC: Primary 20; 14
In this book, the authors explain the construction (due to Gaitsgory) of the ”central sheaves“ on the affine flag variety of a reductive algebraic group associated with the representations of the Langlands dual group. These objects are the categorical counterpart of the Bernstein description of the center of the affine Hecke algebra. They play a crucial role in many constructions related to the geometric Langlands program, some of which have important applications to the representation theory of reductive algebraic groups and associated quantum groups.
The authors also explain the proof of the main properties of these objects (in particular, the filtration by Wakimoto sheaves) for arbitrary coefficients.
Finally, the authors present in detail the construction of an equivalence of categories due to Arkhipov-Bezrukavnikov relating certain derived categories of constructible sheaves on the affine flag variety and coherent sheaves on the Springer resolution of the dual group, in which central sheaves play a key role.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.
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In this book, the authors explain the construction (due to Gaitsgory) of the ”central sheaves“ on the affine flag variety of a reductive algebraic group associated with the representations of the Langlands dual group. These objects are the categorical counterpart of the Bernstein description of the center of the affine Hecke algebra. They play a crucial role in many constructions related to the geometric Langlands program, some of which have important applications to the representation theory of reductive algebraic groups and associated quantum groups.
The authors also explain the proof of the main properties of these objects (in particular, the filtration by Wakimoto sheaves) for arbitrary coefficients.
Finally, the authors present in detail the construction of an equivalence of categories due to Arkhipov-Bezrukavnikov relating certain derived categories of constructible sheaves on the affine flag variety and coherent sheaves on the Springer resolution of the dual group, in which central sheaves play a key role.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.
