arXiv subjects

Takuya Miyamoto

Publications and source records attributed to Takuya Miyamoto.

3 recordsLinked to original sources

arXiv2025

Finiteness of leaps of modules of integrable derivations of algebras of finite type

We prove the finiteness of leaps of modules of $m$-integrable derivations for algebras essentially of finite type and, more generally, for schemes essentially of finite type over an algebraically closed field of positive characteristic. This provides an affirmative answer to a question posed by L. Narv\'aez Macarro. As an application, we establish the coherence of the module of $\infty$-integrable derivations.

math.AG↗

arXiv2025

Hasse-Schmidt derivations and locally trivial deformations in positive characteristic

In this paper, we first study the lifting problem of Hasse-Schmidt derivations and then apply the results to the theory of locally trivial deformations of algebraic schemes in positive characteristic. As an application, we construct an algebraic curve whose locally trivial deformation functor does not satisfy Schlessinger's condition (H1).

math.AG↗

arXiv2025

Pathology of formal locally-trivial deformations in positive characteristic

We construct explicit examples that are algebraic varieties in positive characteristic to show that locally trivial moduli functors do not always satisfy Schlessinger's condition $(H_1)$ in [3], in contrast to the complex/characteristic $0$ case. The first example is an algebraic curve, and the second is a normal rational projective surface with only one rational double point.

math.AG↗