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Quasi-constant characters: Motivation, classification and applications
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 22018 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 339, p. 336-366Article in journal (Refereed) Published
Abstract [en]

In [131, initially motivated by questions about the Hodge line bundle of a Hodge-type Shimura variety, we singled out a generalization of the notion of minuscule character which we termed quasi-constant. Here we prove that the character of the Hodge line bundle is always quasi-constant. Furthermore, we classify the quasi-constant characters of an arbitrary connected, reductive group over an arbitrary field. As an application, we observe that, if mu is a quasi-constant cocharacter of an F-p-group G, then our construction of group-theoretical Hasse invariants in loc. cit. applies to the stack G-Zip(mu), without any restrictions on p, even if the pair (G, mu) is not of Hodge type and even if mu is not minuscule. We conclude with a more speculative discussion of some further motivation for considering quasi-constant cocharacters in the setting of our program outlined in loc. cit.

Place, publisher, year, edition, pages
2018. Vol. 339, p. 336-366
Keywords [en]
Quasi-constant, Shimura varieties, Hodge line bundle, G-Zips, Minuscule, Cominuscule
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-162831DOI: 10.1016/j.aim.2018.09.026ISI: 000449140700008OAI: oai:DiVA.org:su-162831DiVA, id: diva2:1269457
Available from: 2018-12-10 Created: 2018-12-10 Last updated: 2018-12-10Bibliographically approved

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