D. Tossici

activity

20052024

collaborators

13 papers

math.AG2024

Unexpected subgroup schemes of PGL_{2,k} in characteristic 2

Bianca Gouthier, Dajano Tossici

If the characteristic of a field $k$ is odd any infinitesimal group scheme of $P G L_{2, k}$ lifts to $S L_{2, k}$ . In this paper, we prove that this is not true in characteristic $2$ a…

math.AG2019

Special groups, versality and the Grothendieck-Serre conjecture

Zinovy Reichstein, Dajano Tossici

Let $k$ be a base field and $G$ be an algebraic group over $k$ . J.-P. Serre defined $G$ to be special if every $G$ -torsor $T \to X$ is locally trivial in the Zariski topology for e…

math.AG2018

Smooth affine group schemes over the dual numbers

Matthieu Romagny, Dajano Tossici

We provide an equivalence between the category of affine, smooth group schemes over the ring of generalized dual numbers $k [I]$ , and the category of extensions of the form $1 \righ…

math.AG2017

Essential dimension of infinitesimal unipotent group schemes

Dajano Tossici

We propose a generalization of Ledet conjecture, which predicts the essential dimension of cyclic $p$ -groups in characteristic $p$ , for finite commutative unipotent group schemes.…

math.AG2016

Essential dimension of group schemes over a local scheme

Dajano Tossici

In this paper we develop the theory of essential dimension of group schemes over an integral base. Shortly we concentrate over a local base. As a consequence of our theory we give…

math.NT2011

Sekiguchi-Suwa theory revisited

Ariane Mézard, Matthieu Romagny, Dajano Tossici

We present an account of the construction by S. Sekiguchi and N. Suwa of a cyclic isogeny of affine smooth group schemes unifying the Kummer and Artin-Schreier-Witt isogenies. We c…