Tsukuba Journal of Mathematics

On the group of extensions Ext1($\mathscr{G}$(λ0), $\mathscr{E}$(λ1, ..., λ n )) over a discrete valuation ring

Takashi Kondo

Abstract

For given group schemes $\mathscr{G}$ 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}$2) → $\mathscr{E}$1, λ2) → $\mathscr{G}$1) → 0, … 0 → $\mathscr{G}$ n ) → $\mathscr{E}$1, ..., λ n ) → $\mathscr{E}$1, ..., λn-1) → 0, … inductively, by calculating the group of extensions Ext1($\mathscr{E}$1, ..., λn-1), $\mathscr{G}$ n )). Here changing the group schemes, we treat the group Ext1($\mathscr{G}$0), $\mathscr{E}$1, ..., λ n )) of extensions for any positive integers n. The case of n = 2, 3 were studied by D. Horikawa and T. Kondo.

Article information

Source
Tsukuba J. Math., Volume 34, Number 2 (2011), 265-294.

Dates
First available in Project Euclid: 8 April 2011

Kondo, Takashi. On the group of extensions Ext 1 ($\mathscr{G}$ (λ 0 ) , $\mathscr{E}$ (λ 1 , ., λ n ) ) over a discrete valuation ring. Tsukuba J. Math. 34 (2011), no. 2, 265--294. doi:10.21099/tkbjm/1302268249. https://projecteuclid.org/euclid.tkbjm/1302268249