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http://hdl.handle.net/1942/30080
Title: | The Frobenius morphism in invariant theory | Authors: | RAEDSCHELDERS, Theo SPENKO, Spela VAN DEN BERGH, Michel |
Issue Date: | 2019 | Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Source: | ADVANCES IN MATHEMATICS, 348, p. 183-254 | Abstract: | Let R be the homogeneous coordinate ring of the Grassmannian G = Gr(2, n) defined over an algebraically closed field of characteristic p > 0. In this paper we give a completely characteristic free description of the decomposition of R, considered as a graded R-p-module, into indecomposables ("Frobenius summands"). As a corollary we obtain a similar decomposition for the Frobenius pushforward of the structure sheaf of G and we obtain in particular that this pushforward is almost never a tilting bundle. On the other hand we show that R provides a "noncommutative resolution" for R-p when p >= n - 2, generalizing a result known to be true for toric varieties. In both the invariant theory and the geometric setting we observe that if the characteristic is not too small the Frobenius summands do not depend on the characteristic in a suitable sense. In the geometric setting this is an explicit version of a general result by Bezrukavnikov and Mirkovid on Frobenius decompositions for partial flag varieties. We are hopeful that it is an instance of a more general "p-uniformity" principle. (C) 2019 Elsevier Inc. All rights reserved. | Notes: | [Raedschelders, Theo] Univ Glasgow, Sch Math & Stat, Glasgow G12 8QQ, Lanark, Scotland. [Spenko, Spela] Vrije Univ Brussel, Dept Wiskunde, Pleinlaan 2, B-1050 Elsene, Belgium. [Van den Bergh, Michel] Univ Hasselt, Dept WNI, Univ Campus, B-3590 Diepenbeek, Belgium. | Keywords: | Invariant theory; Frobenius summand; FFRT; Grassmannian; Tilting bundle; Noncommutativc resolution;Frobenius summand;FFRT | Document URI: | http://hdl.handle.net/1942/30080 | ISSN: | 0001-8708 | e-ISSN: | 1090-2082 | DOI: | 10.1016/j.aim.2019.03.013 | ISI #: | 000466835800007 | Rights: | 2019 Elsevier Inc. All rights reserved. | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2020 |
Appears in Collections: | Research publications |
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