Primitively generated Hopf orders in characteristic p

References

• Abrashkin, V. (2006). Galois modules arising from Faltings’s strict modules. Compos. Math. 142(4):867–888.
   Web of Science ®Google Scholar
• Byott, N. P. (1993). Cleft extensions of Hopf algebras. II. Proc. London Math. Soc. (3) 67(2):277–304.
   Google Scholar
• Byott, N. P. (2004). Monogenic Hopf orders and associated orders of valuation rings. J. Algebra 275(2):575–599.
   Web of Science ®Google Scholar
• Childs, L. N. (2000). Taming wild extensions: Hopf algebras and local Galois module theory, Vol. 80 of Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society.
   Google Scholar
• Childs, L. N., Greither, C., Moss, D. J., Sauerberg, J., Zimmermann, K. (1998). Hopf algebras, polynomial formal groups, and Raynaud orders. Mem. Amer. Math. Soc. 136(651):viii+118.
   Web of Science ®Google Scholar
• Childs, L. N., Smith, III (2005). Dual Hopf orders in group rings of elementary abelian p-groups. J. Algebra 294(2):489–518.
   Web of Science ®Google Scholar
• Childs, L. N., Underwood, R. G. (2003). Cyclic Hopf orders defined by isogenies of formal groups. Amer. J. Math. 125(6):1295–1334.
   Web of Science ®Google Scholar
• Childs, L. N., Underwood, R. G. (2004). Duals of formal group Hopf orders in cyclic groups. Illinois J. Math. 48(3):923–940.
   Web of Science ®Google Scholar
• de Jong, A. J. (1993). Finite locally free group schemes in characteristic p and Dieudonné modules. Invent. Math. 114(1):89–137.
   Web of Science ®Google Scholar
• Fontaine, J.-M. (1975). Groupes finis commutatifs sur les vecteurs de Witt. C. R. Acad. Sci. Paris Sér. A-B, 280:Ai, A1423–A1425.
   Google Scholar
• Greither, C. (1992). Extensions of finite group schemes, and Hopf Galois theory over a complete discrete valuation ring. Extensions of finite group schemes, and Hopf Galois theory over a complete discrete valuation ring, 210(1):37–67.
   Google Scholar
• Kisin, M. (2007). Modularity of 2-dimensional Galois representations. In: Current developments in mathematics, Vol. 2005, Somerville, MA: International Press, pp. 191–230.
   Google Scholar
• Koch, A. (2007). Hopf orders via Breuil modules. J. Algebra 317(1):291–305.
   Web of Science ®Google Scholar
• Koch, A. (2012). Breuil-Kisin modules and Hopf orders in cyclic group rings. Commun. Algebra 40(2):607–631.
   Web of Science ®Google Scholar
• Koch, A., Malagon, A. (2007). p-adic order bounded group valuations on abelian groups. Glasg. Math. J. 49(2):269–279.
   Web of Science ®Google Scholar
• Larson, R. G. (1976). Hopf algebra orders determined by group valuations. J. Algebra 38(2):414–452.
   Web of Science ®Google Scholar
• Lau, E. (2010). Frames and finite group schemes over complete regular local rings. Doc. Math. 15:545–569.
   Web of Science ®Google Scholar
• Mézard, A., Romagny, M., Tossici, D. (2013). Models of group schemes of roots of unity. Ann. Inst. Fourier (Grenoble) 63(3):1055–1135.
   Web of Science ®Google Scholar
• Romagny, M. (2012). Effective models of group schemes. J. Algebraic Geom. 21(4):643–682.
   Web of Science ®Google Scholar
• Tate, J., Oort, F. (1970). Group schemes of prime order. Ann. Sci. École Norm. Sup. (4) 3:1–21.
   Google Scholar
• Tossici, D. (2008). Effective models and extension of torsors over a discrete valuation ring of unequal characteristic. Int. Math. Res. Not. IMRN, pages Art. ID rnn111, 68.
   Google Scholar
• Tossici, D. (2010). Models of μp2,K over a discrete valuation ring. J. Algebra 323(7):1908–1957. With an appendix by Xavier Caruso.
   Web of Science ®Google Scholar
• Underwood, R. G., Childs, L. N. (2006). Duality for Hopf orders. Trans. Amer. Math. Soc. 358(3):1117–1163.
   Web of Science ®Google Scholar
• Underwood, R. G. (1994). R-Hopf algebra orders in KCp2. J. Algebra 169(2):418–440.
   Web of Science ®Google Scholar
• Underwood, R. G. (2006). Realizable Hopf orders in KC8. Int. Math. Forum 1(17–20):833–851.
   Google Scholar
• Underwood, R. G. (2008). Realizable Hopf orders in KCp3. J. Algebra 319(11):4426–4455.
   Web of Science ®Google Scholar
• Underwood, R. (1996). The valuative condition and R-Hopf algebra orders in KCp3. The valuative condition and R-Hopf algebra orders in $K{C}_{p^3}$, 118(4):701–743.
   Google Scholar