Dat, J.-F., Helm, D., Kurinczuk, R. orcid.org/0000-0002-9356-4563 et al. (1 more author) (2025) Moduli of Langlands parameters. Journal of the European Mathematical Society. ISSN 1435-9855
Abstract
Let F be a non-archimedean local field of residue characteristic p, let ˆ G be a split reductive group scheme over Z[1 p] with an action of WF, and let G L denote the semidirect product ˆ G ⋊ WF. We construct a moduli space of Langlands parameters WF → G L ,and show that it is locally of finite type and flat over Z[1 p], and that it is a reduced local complete intersection. We give parameterizations of the connected components and the irreducible components of the geometric fibers of this space, and parameterizations of the connected components of the total space over Z[1 p] (under mild hypotheses) and over Zℓ for ℓ= p. In each case, we show precisely how each connected component identifies with the “principal” connected component attached to a smaller split reductive group scheme. Finally, we study the GIT quotient of this space by ˆ G and give a description of its fibers up to homeomorphism, and a complete description of its ring of functions after inverting an explicit finite set of primes depending only on G L .
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2025 European Mathematical Society. This is an author-produced version of a paper subsequently published in Journal of the European Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematical and Physical Sciences |
Funding Information: | Funder Grant number Engineering and Physical Sciences Research Council EP/V001930/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 16 Oct 2024 15:58 |
Last Modified: | 17 Mar 2025 14:31 |
Status: | Published online |
Publisher: | EMS Press |
Refereed: | Yes |
Identification Number: | 10.4171/jems/1599 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:218242 |