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arxiv: 1609.03187 · v1 · pith:U5NKXSJHnew · submitted 2016-09-11 · 🧮 math.NT

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

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keywords mathbbpresentationsemi-simplechevalleycongruenceconnectedfirstgroup
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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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