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On the mod p reduction of orthogonal representations

  • Jean-Pierre SerreEmail author
Chapter
Part of the Progress in Mathematics book series (PM, volume 326)

Abstract

We show that the reduction mod p of an orthogonal, or symplectic, linear representation of a group (or of an algebra with involution) is also orthogonal, or symplectic. The proof makes use of a (perhaps new) construction: the lower and upper “middles” of a pair of lattices.

Keywords

Brauer-Nesbitt lattice middle orthogonal semisimplification 

Mathematics Subject Classification (2010):

20Cxx 13F30 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Collége de FranceParisFrance

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