Relevant bibliographies by topics / Group schemes, torsors, Witt vectors

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Academic literature on the topic 'Group schemes, torsors, Witt vectors'

Author: Grafiati
Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Group schemes, torsors, Witt vectors"

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Anschütz, Johannes. "Extending torsors on the punctured Spec(A inf)." Journal für die reine und angewandte Mathematik (Crelles Journal) 2022, no. 783 (January 6, 2022): 227–68. http://dx.doi.org/10.1515/crelle-2021-0077.

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Abstract We prove that torsors under parahoric group schemes on the punctured spectrum of Fontaine’s ring A inf {A_{\mathrm{inf}}} , extend to the whole spectrum. Using descent we can extend a similar result for the ring 𝔖 {\mathfrak{S}} of Kisin and Pappas to full generality. Moreover, we treat similarly the case of equal characteristic. As applications we extend results of Ivanov on exactness of the loop functor and present the construction of a canonical specialization map from the B dR + {B^{+}_{\mathrm{dR}}} -affine Grassmannian to the Witt vector affine flag variety.
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2

Abrashkin, V. A. "GALOIS MODULI OF PERIOD $p$ GROUP SCHEMES OVER A RING OF WITT VECTORS." Mathematics of the USSR-Izvestiya 31, no. 1 (February 28, 1988): 1–46. http://dx.doi.org/10.1070/im1988v031n01abeh001042.

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3

Biswas, Indranil, and João Pedro P. Dos Santos. "Vector bundles trivialized by proper morphisms and the fundamental group scheme." Journal of the Institute of Mathematics of Jussieu 10, no. 2 (February 24, 2010): 225–34. http://dx.doi.org/10.1017/s1474748010000071.

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AbstractLet X be a smooth projective variety defined over an algebraically closed field k. Nori constructed a category of vector bundles on X, called essentially finite vector bundles, which is reminiscent of the category of representations of the fundamental group (in characteristic zero). In fact, this category is equivalent to the category of representations of a pro-finite group scheme which controls all finite torsors. We show that essentially finite vector bundles coincide with those which become trivial after being pulled back by some proper and surjective morphism to X.
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4

Bauer, Tilman. "Affine and formal abelian group schemes on $p$-polar rings." MATHEMATICA SCANDINAVICA 128, no. 1 (February 24, 2022). http://dx.doi.org/10.7146/math.scand.a-129704.

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We show that the functor of $p$-typical co-Witt vectors on commutative algebras over a perfect field $k$ of characteristic $p$ is defined on, and in fact only depends on, a weaker structure than that of a $k$-algebra. We call this structure a $p$-polar $k$-algebra. By extension, the functors of points for any $p$-adic affine commutative group scheme and for any formal group are defined on, and only depend on, $p$-polar structures. In terms of abelian Hopf algebras, we show that a cofree cocommutative Hopf algebra can be defined on any $p$-polar $k$-algebra $P$, and it agrees with the cofree commutative Hopf algebra on a commutative $k$-algebra $A$ if $P$ is the $p$-polar algebra underlying $A$; a dual result holds for free commutative Hopf algebras on finite $k$-coalgebras.
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Dissertations / Theses on the topic "Group schemes, torsors, Witt vectors"

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TOSSICI, DAJANO. "Group schemes of order p^2 and extension of Z/p^2Z-torsors." Doctoral thesis, Università di Roma Tre, 2008. http://hdl.handle.net/10281/20961.

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In this work we study finite group schemes over a discrete valuation ring of unequal characteristic which are isomorphic to the group scheme of p^2-roots of unity, where p is the characteristic of the residue field of R, on the generic fiber. And we apply this to the study of the degeneration, from caracteristic p to caracteristic 0, of torsors under the cyclic group of order p^2.
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