Abstract

ZHANG, Robin. Orthogonal groups over fields of positive characteristic. Rev. Mat [online]. 2022, vol.29, n.2, pp.159-176. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v29i2.49254.

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.

Keywords : orthogonal group; positive characteristic; bilinear form; quadratic form; Arf invariant; Dickson invariant; spinorial kernel.

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