Generic extensions and generic polynomials for linear algebraic groups

Eric Chen; J. T. Ferrara; Liam Mazurowski

doi:10.1016/j.jalgebra.2016.04.027

Generic extensions and generic polynomials for linear algebraic groups

Eric Chen
, J. T. Ferrara
, Liam Mazurowski

Research output: Contribution to journal › Article › peer-review

Abstract

We construct generic extensions and polynomials for certain linear algebraic groups over finite fields. In particular, we show the existence of generic polynomials for the cyclic group C_2m in characteristic p for all odd primes p.

Original language	English (US)
Pages (from-to)	1-24
Number of pages	24
Journal	Journal of Algebra
Volume	461
DOIs	https://doi.org/10.1016/j.jalgebra.2016.04.027
State	Published - Sep 1 2016
Externally published	Yes

Keywords

Galois cohomology
Generic extensions
Generic polynomials
Linear algebraic groups

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.1016/j.jalgebra.2016.04.027

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title = "Generic extensions and generic polynomials for linear algebraic groups",

abstract = "We construct generic extensions and polynomials for certain linear algebraic groups over finite fields. In particular, we show the existence of generic polynomials for the cyclic group C2m in characteristic p for all odd primes p.",

keywords = "Galois cohomology, Generic extensions, Generic polynomials, Linear algebraic groups",

author = "Eric Chen and Ferrara, \{J. T.\} and Liam Mazurowski",

note = "This research was conducted at the 2015 Louisiana State University Research Experience for Undergraduates supported by the National Science Foundation REU Grant DMS 0648064 . We thank professor J. Morales for guiding us through the project.",

year = "2016",

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doi = "10.1016/j.jalgebra.2016.04.027",

language = "English (US)",

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journal = "Journal of Algebra",

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AU - Chen, Eric

AU - Ferrara, J. T.

AU - Mazurowski, Liam

N1 - This research was conducted at the 2015 Louisiana State University Research Experience for Undergraduates supported by the National Science Foundation REU Grant DMS 0648064 . We thank professor J. Morales for guiding us through the project.

PY - 2016/9/1

Y1 - 2016/9/1

N2 - We construct generic extensions and polynomials for certain linear algebraic groups over finite fields. In particular, we show the existence of generic polynomials for the cyclic group C2m in characteristic p for all odd primes p.

AB - We construct generic extensions and polynomials for certain linear algebraic groups over finite fields. In particular, we show the existence of generic polynomials for the cyclic group C2m in characteristic p for all odd primes p.

KW - Galois cohomology

KW - Generic extensions

KW - Generic polynomials

KW - Linear algebraic groups

UR - https://www.scopus.com/pages/publications/84968807698

UR - https://www.scopus.com/pages/publications/84968807698#tab=citedBy

U2 - 10.1016/j.jalgebra.2016.04.027

DO - 10.1016/j.jalgebra.2016.04.027

M3 - Article

AN - SCOPUS:84968807698

SN - 0021-8693

VL - 461

SP - 1

EP - 24

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Generic extensions and generic polynomials for linear algebraic groups

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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