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Field reduction and linear sets in finite geometry

Michel Lavrauw and Geertrui Van de Voorde UGent (2015) Contemporary Mathematics. In Contemporary Mathematics 632. p.271-293
abstract
Based on the simple and well understood concept of subfields in a finite field, the technique called 'field reduction' has proved to be a very useful and powerful tool in finite geometry. In this paper we elaborate on this technique. Field reduction for projective and polar spaces is formalised and the links with Desarguesian spreads and linear sets are explained in detail. Recent results and some fundamental questions about linear sets and scattered spaces are studied. The relevance of field reduction is illustrated by discussing applications to blocking sets and semifields.
Please use this url to cite or link to this publication:
author
organization
year
type
conference (proceedingsPaper)
publication status
published
subject
keyword
Field reduction, Desarguesian spread, Segre variety, linear set, scattered spaces, SMALL BLOCKING SETS, POLAR SPACES, SEMIFIELDS, PG(N, SPREADS, NUMBER
in
Contemporary Mathematics
editor
G Kyureghyan, GL Mullen and A Pott
series title
Contemporary Mathematics
volume
632
issue title
Topics in finite fields
pages
271 - 293
publisher
American Mathematical Society
place of publication
Providence, RI, USA
conference name
11th International conference on Finite Fields and their Applications
conference location
Magdeburg, Germany
conference start
2013-07-22
conference end
2013-07-26
Web of Science type
Proceedings Paper
Web of Science id
000361092200020
ISSN
0271-4132
ISBN
9780821898604
DOI
10.1090/conm/632/12633
language
English
UGent publication?
yes
classification
P1
copyright statement
I have transferred the copyright for this publication to the publisher
id
7161211
handle
http://hdl.handle.net/1854/LU-7161211
date created
2016-03-24 10:41:06
date last changed
2017-01-02 09:53:20
@inproceedings{7161211,
  abstract     = {Based on the simple and well understood concept of subfields in a finite field, the technique called 'field reduction' has proved to be a very useful and powerful tool in finite geometry. In this paper we elaborate on this technique. Field reduction for projective and polar spaces is formalised and the links with Desarguesian spreads and linear sets are explained in detail. Recent results and some fundamental questions about linear sets and scattered spaces are studied. The relevance of field reduction is illustrated by discussing applications to blocking sets and semifields.},
  author       = {Lavrauw, Michel and Van de Voorde, Geertrui},
  booktitle    = {Contemporary Mathematics},
  editor       = {Kyureghyan, G and Mullen, GL and Pott, A},
  isbn         = {9780821898604},
  issn         = {0271-4132},
  keyword      = {Field reduction,Desarguesian spread,Segre variety,linear set,scattered spaces,SMALL BLOCKING SETS,POLAR SPACES,SEMIFIELDS,PG(N,SPREADS,NUMBER},
  language     = {eng},
  location     = {Magdeburg, Germany},
  pages        = {271--293},
  publisher    = {American Mathematical Society},
  title        = {Field reduction and linear sets in finite geometry},
  url          = {http://dx.doi.org/10.1090/conm/632/12633},
  volume       = {632},
  year         = {2015},
}

Chicago
Lavrauw, Michel, and Geertrui Van de Voorde. 2015. “Field Reduction and Linear Sets in Finite Geometry.” In Contemporary Mathematics, ed. G Kyureghyan, GL Mullen, and A Pott, 632:271–293. Providence, RI, USA: American Mathematical Society.
APA
Lavrauw, M., & Van de Voorde, G. (2015). Field reduction and linear sets in finite geometry. In G. Kyureghyan, G. Mullen, & A. Pott (Eds.), Contemporary Mathematics (Vol. 632, pp. 271–293). Presented at the 11th International conference on Finite Fields and their Applications, Providence, RI, USA: American Mathematical Society.
Vancouver
1.
Lavrauw M, Van de Voorde G. Field reduction and linear sets in finite geometry. In: Kyureghyan G, Mullen G, Pott A, editors. Contemporary Mathematics. Providence, RI, USA: American Mathematical Society; 2015. p. 271–93.
MLA
Lavrauw, Michel, and Geertrui Van de Voorde. “Field Reduction and Linear Sets in Finite Geometry.” Contemporary Mathematics. Ed. G Kyureghyan, GL Mullen, & A Pott. Vol. 632. Providence, RI, USA: American Mathematical Society, 2015. 271–293. Print.