Abstract
In this note we show how to construct a factorizable line bundle on the affine Grassmannian of a group G starting from a Brylinski-Deligne datum, which is an extension of G by the Zaraski-sheafified \(K_2\).
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Acknowledgements
Special thanks are due to Sasha Beilinson, who suggested to me the key ideas to overcome the obstacles in carrying out the construction in this paper (to use the full K-theory spectrum, the “raising to the power” trick, and the comparison with motivic cohomology). No less importantly, I would like to thank him for his patience over the years in answering my persistent questions, along with teaching me the basics of motivic cohomology. I am also very grateful to S. Bloch, D. Clausen, E. Elmanto, H. Esnault, M. Hopkins, M. Kerr, J. Lurie, A. Mathew and C. Weibel for patiently answering my questions on K-theory and motivic cohomology. Finally, I would like to thank my graduate student Y. Zhao for catching the original mistake in [1], as well as for numerous subsequent discussions on the subject. I am additionally grateful to him and J. Tao for taking up (what appears in the present paper as) Conjecture 6.1.2 as a project. The author is supported by NSF grant DMS-1063470. He has also received support from ERC Grant 669655.
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Gaitsgory, D. Parameterization of factorizable line bundles by K-theory and motivic cohomology. Sel. Math. New Ser. 26, 44 (2020). https://doi.org/10.1007/s00029-020-00565-7
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DOI: https://doi.org/10.1007/s00029-020-00565-7