On Serre’s injectivity question and norm principle
Nivedita Bhaskhar
Emory University, Atlanta, USA
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Abstract
Let be a field of characteristic not . We give a positive answer to Serre's injectivity question for any smooth connected reductive -group whose Dynkin diagram contains connected components only of type , or . We do this by relating Serre's question to the norm principles proved by Barquero and Merkurjev. We give a scalar obstruction defined up to spinor norms whose vanishing will imply the norm principle for the non-trialitarian case and yield a positive answer to Serre's question for connected reductive -groups whose Dynkin diagrams contain components of (non-trialitarian) type too. We also investigate Serre's question for quasi-split reductive -groups.
Cite this article
Nivedita Bhaskhar, On Serre’s injectivity question and norm principle. Comment. Math. Helv. 91 (2016), no. 1, pp. 145–161
DOI 10.4171/CMH/381