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2005 Infinite dimensional algebraic geometry: algebraic structures on {$p$}-adic groups and their homogeneous spaces
William J. Haboush
Tohoku Math. J. (2) 57(1): 65-117 (2005). DOI: 10.2748/tmj/1113234835

Abstract

Let $k$ denote the algebraic closure of the finite field, $\mathbb F_p,$ let $\mathcal O$ denote the Witt vectors of $k$ and let $K$ denote the fraction field of this ring. In the first part of this paper we construct an algebraic theory of ind-schemes that allows us to represent finite $K$ schemes as infinite dimensional $k$-schemes and we apply this to semisimple groups. In the second part we construct spaces of lattices of fixed discriminant in the vector space $K^n.$ We determine the structure of these schemes. We devote particular attention to lattices of fixed discriminant in the lattice, $p^{-r}\mathcal O^n,$ computing the Zariski tangent space to a lattice in this scheme and determining the singular points.

Citation

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William J. Haboush. "Infinite dimensional algebraic geometry: algebraic structures on {$p$}-adic groups and their homogeneous spaces." Tohoku Math. J. (2) 57 (1) 65 - 117, 2005. https://doi.org/10.2748/tmj/1113234835

Information

Published: 2005
First available in Project Euclid: 11 April 2005

MathSciNet: MR2113991
zbMATH: 1119.14004
Digital Object Identifier: 10.2748/tmj/1113234835

Subjects:
Primary: 20G25
Secondary: 14L15 , 20G99

Keywords: group schemes , Hilbert class field , lattices , Witt vectors

Rights: Copyright © 2005 Tohoku University

Vol.57 • No. 1 • 2005
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