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arXiv · 1609.03187

Presentation of the Iwasawa algebra of the first congruence kernel of a semi-simple, simply connected Chevalley group over $\mathbb{Z}_p$

Jishnu Ray
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Abstract

It is a general principle that objects coming from semi-simple, simply connected (split) groups have explicit presentations like Serre's presentation of semi-simple algebras and Steinberg's presentation of Chevalley groups. In this paper we give an explicit presentation (by generators and relations) of the Iwasawa algebra for the first congruence kernel of a semi-simple, simply connected Chevalley group over $\mathbb{Z}_p$, extending the proof given by Clozel for the group $\Gamma_1(SL_2(\mathbb{Z}_p))$, the first congruence kernel of $SL_2(\mathbb{Z}_p)$ for primes $p>2$.

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Jishnu Ray. 2016-09-11. Presentation of the Iwasawa algebra of the first congruence kernel of a semi-simple, simply connected Chevalley group over $\mathbb{Z}_p$. https://arxiv.org/abs/1609.03187

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