Proceedings of the Japan Academy, Series A, Mathematical Sciences

On the topology of relative orbits for actions of algebraic groups over complete fields

Dao Phuong Bac and Nguyen Quoc Thang

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Abstract

We investigate the problem of equipping a topology on cohomology groups (sets) in its relation with the problem of closedness of (relative) orbits for the action of algebraic groups on affine varieties defined over complete, especially $\mathfrak{p}$-adic fields and give some applications.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 86, Number 8 (2010), 133-138.

Dates
First available in Project Euclid: 4 October 2010

Permanent link to this document
https://projecteuclid.org/euclid.pja/1286198322

Digital Object Identifier
doi:10.3792/pjaa.86.133

Mathematical Reviews number (MathSciNet)
MR2721858

Zentralblatt MATH identifier
1217.14031

Subjects
Primary: 14L24: Geometric invariant theory [See also 13A50]
Secondary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 20G15: Linear algebraic groups over arbitrary fields

Keywords
Closed orbits local fields algebraic group actions

Citation

Bac, Dao Phuong; Thang, Nguyen Quoc. On the topology of relative orbits for actions of algebraic groups over complete fields. Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), no. 8, 133--138. doi:10.3792/pjaa.86.133. https://projecteuclid.org/euclid.pja/1286198322


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