Zobrazeno 1 - 10
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pro vyhledávání: '"Ohkubo, Shun"'
Autor:
Ohkubo, Shun
One of the phenomena peculiar in the theory of $p$-adic differential equations is that solutions $f$ of $p$-adic differential equations defined on open discs may satisfy growth conditions at the boundaries. This phenomenon is first studied by Dwork,
Externí odkaz:
http://arxiv.org/abs/2411.16562
Autor:
Ohkubo, Shun
Let $K$ be a complete non-archimedean valuation field of characteristic $0$, with non-trivial valuation, equipped with (possibly multiple) commuting bounded derivations. We prove a decomposition theorem for finite differential modules over $K$, where
Externí odkaz:
http://arxiv.org/abs/2404.16291
Autor:
Ohkubo, Shun
In this paper, we study the logarithmic growth (log-growth) filtration, a mysterious invariant found by B. Dwork, for $(\varphi,\nabla)$-modules over the bounded Robba ring. The main result is a proof of a conjecture proposed by B. Chiarellotto and N
Externí odkaz:
http://arxiv.org/abs/1809.04065
Autor:
Ohkubo, Shun
For a $p$-adic differential equation solvable in an open disc (in a $p$-adic sense), around 1970, Dwork proves that the solutions satisfy a certain growth condition on the boundary. Dwork also conjectures that a similar phenomenon should be observed
Externí odkaz:
http://arxiv.org/abs/1801.00771
Autor:
Ohkubo, Shun
We study the asymptotic behavior of solutions of Frobenius equations defined over the ring of overconvergent series. As an application, we prove Chiarellotto-Tsuzuki's conjecture on the rationality and right continuity of Dwork's logarithmic growth f
Externí odkaz:
http://arxiv.org/abs/1502.03804
Autor:
Ohkubo, Shun
In this paper, we answer a question due to Y. Andr\'e related to B. Dwork's conjecture on a specialization of the logarithmic growth of solutions of $p$-adic linear differential equations. Precisely speaking, we explicitly construct a $\nabla$-module
Externí odkaz:
http://arxiv.org/abs/1312.7789
Autor:
Ohkubo, Shun
Let $K$ be a complete discrete valuation field of mixed characteristic $(0,p)$ with residue field $k_K$ such that $[k_K:k_K^p]=p^d<\infty$. Let $G_K$ be the absolute Galois group of $K$ and $\rho:G_K\to GL_h(\Q_p)$ a $p$-adic representation. When $k_
Externí odkaz:
http://arxiv.org/abs/1307.8107
Autor:
Ohkubo, Shun
Publikováno v:
Algebra Number Theory 9 (2015) 1881-1954
Let $K$ be a complete discrete valuation field of mixed characteristic $(0,p)$, whose residue field may not be perfect, and $G_K$ the absolute Galois group of $K$. In the first part of this paper, we prove that Scholl's generalization of fields of no
Externí odkaz:
http://arxiv.org/abs/1307.8110
Autor:
Ohkubo, Shun
Publikováno v:
Algebra Number Theory 7 (2013) 1977-2037
Let K be a complete discrete valuation field of mixed characteristic (0,p) and G_K the absolute Galois group of K. In this paper, we will prove the p-adic monodromy theorem for p-adic representations of G_K without any assumption on the residue field
Externí odkaz:
http://arxiv.org/abs/1205.3457
Autor:
Ohkubo, Shun
In Sen's theory in the imperfect residue field case, Brinon defined a functor from the category of C_p-representations to the category of linear representations of certain Lie algebra. We give a comparison theorem between the continuous Galois cohomo
Externí odkaz:
http://arxiv.org/abs/0905.2151