Geodesic
The Tate--Oort Group Scheme $\mathbb {TO}_p$
Informatics and Automation, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 267-290.

Voir la notice de l'article provenant de la source Math-Net.Ru

Over an algebraically closed field of characteristic $p$, there are three group schemes of order $p$, namely the ordinary cyclic group $\mathbb Z/p$, the multiplicative group $\boldsymbol \mu _p\subset \mathbb G_\mathrm{m}$ and the additive group $\boldsymbol \alpha _p\subset \mathbb G_\mathrm{a}$. The Tate–Oort group scheme $\mathbb {TO}_p$ puts these into one happy family, together with the cyclic group of order $p$ in characteristic zero. This paper studies a simplified form of $\mathbb {TO}_p$, focusing on its representation theory and basic applications in geometry. A final section describes more substantial applications to varieties having $p$-torsion in $\mathrm {Pic}^\tau $, notably the $5$-torsion Godeaux surfaces and Calabi–Yau threefolds obtained from $\mathbb {TO}_5$-invariant quintics. 
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     author = {Miles Reid},
     title = {The {Tate--Oort} {Group} {Scheme} $\mathbb {TO}_p$},
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     volume = {307},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2019_307_a14/}
}
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Miles Reid. The Tate--Oort Group Scheme $\mathbb {TO}_p$. Informatics and Automation, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 267-290. http://geodesic.mathdoc.fr/item/TRSPY_2019_307_a14/

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