Abstract
For given group schemes $\mathscr{G}$(λ i ) (i = 1, 2, ...) deforming the additive group scheme G a to the multiplicative group scheme G m , T. Sekiguchi and N. Suwa constructed extensions: 0 → $\mathscr{G}$(λ2) → $\mathscr{E}$(λ1, λ2) → $\mathscr{G}$(λ1) → 0, … 0 → $\mathscr{G}$(λ n ) → $\mathscr{E}$(λ1, ..., λ n ) → $\mathscr{E}$(λ1, ..., λn-1) → 0, … inductively, by calculating the group of extensions Ext1($\mathscr{E}$(λ1, ..., λn-1), $\mathscr{G}$(λ n )). Here changing the group schemes, we treat the group Ext1($\mathscr{G}$(λ0), $\mathscr{E}$(λ1, ..., λ n )) of extensions for any positive integers n. The case of n = 2, 3 were studied by D. Horikawa and T. Kondo.
Citation
Takashi Kondo. "On the group of extensions Ext1($\mathscr{G}$(λ0), $\mathscr{E}$(λ1, ..., λ n )) over a discrete valuation ring." Tsukuba J. Math. 34 (2) 265 - 294, February 2011. https://doi.org/10.21099/tkbjm/1302268249
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