Keywords
positive characteristic
bilinear form
quadratic form
Arf invariant
Dickson invariant
spinorial kernel
grupo ortogonal
característica positiva
forma bilineal
forma cuadrática
invariante de Arf
invariante de Dickson
núcleo espinorial
How to Cite
Abstract
This exposition examines the theory of orthogonal groups and their subgroups over fields of positive characteristic, which has recently been used as an important tool in the study of automorphic forms and Langlands functionality. We present the classification of orthogonal groups over a finite field using the theory of bilinear forms and quadratic forms in positive characteristic. Using the determinant and spinor norm when the characteristic of F is odd and using the Dickson invariant when the characteristic of F is even, we also look at special subgroups of the orthogonal group.
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