Journal article
Deformations with respect to an algebraic group
Illinois journal of mathematics, Vol.47(3), pp.899-919
07/01/2003
DOI: 10.1215/ijm/1258138200
Abstract
Let $\mathcal{G}$ be a smooth linear algebraic group over the ring of Witt vectors of a finite field $k$. In this paper, we study deformations of representations of a profinite group into the points $\mathcal{G}(k)$ of $\mathcal{G}$ over $k$. We show that the $\mathcal{G}$-deformation functor has a versal deformation ring, and we generalize criteria of Tilouine concerning when this ring is universal. If $\mathcal{G}$ is an algebraic subgroup of $\mathrm{GL}_n$, we study when the $\mathcal{G}$-deformation functor is a subfunctor of the $\mathrm{GL}_n$-deformation functor studied by Mazur. When $\mathcal{G}$ is an orthogonal group, this leads to studying versal versions of results of Serre and Fröhlich about the connection between Stiefel-Whitney classes, spinor norms and Hasse-Witt invariants of orthogonal Galois representations.
Details
- Title: Subtitle
- Deformations with respect to an algebraic group
- Creators
- Frauke M BleherTed Chinburg
- Resource Type
- Journal article
- Publication Details
- Illinois journal of mathematics, Vol.47(3), pp.899-919
- Publisher
- Duke University Press
- DOI
- 10.1215/ijm/1258138200
- ISSN
- 0019-2082
- eISSN
- 1945-6581
- Language
- English
- Date published
- 07/01/2003
- Academic Unit
- Mathematics
- Record Identifier
- 9984240866102771
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