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Field reduction and linear sets in finite geometry

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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.
Keywords
Field reduction, Desarguesian spread, Segre variety, linear set, scattered spaces, SMALL BLOCKING SETS, POLAR SPACES, SEMIFIELDS, PG(N, SPREADS, NUMBER

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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.
@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},
}

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