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Reference.org
Fundamental group scheme
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<p>In mathematics, the fundamental group scheme is a <a href="/facts/Group_scheme/bJW14FE2">group scheme</a> canonically attached to a <a href="/facts/Scheme_(mathematics)/c7uSqGqL">scheme</a> over a Dedekind scheme (e.g. the spectrum of a <a href="/facts/Field_(mathematics)/xAjAS4ko">field</a> or the spectrum of a <a href="/facts/Discrete_valuation_ring/DaHoTBSH">discrete valuation ring</a>). It is a generalisation of the <a href="/facts/%C3%89tale_fundamental_group/9LKl4Lzp">étale fundamental group</a>. Although its existence was conjectured by <a href="/facts/Alexander_Grothendieck/jLQGPY7M">Alexander Grothendieck</a>, the first proof of its existence is due, for schemes defined over fields, to <a href="/facts/Madhav_V._Nori/KXBk0ylG">Madhav Nori</a>. A proof of its existence for schemes defined over Dedekind schemes is due to <a href="/facts/Marco_Antei/qAPJunrR">Marco Antei</a>, Michel Emsalem and Carlo Gasbarri. </p>