Zobrazeno 1 - 10
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pro vyhledávání: '"Shimomoto, Kazuma"'
Autor:
Shimomoto, Kazuma
The purpose of this paper is to explain a method on the generalization of the Bertini-type theorem on standard graded rings to the non-standard graded case of certain type.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/2312.10800
Autor:
Horiuchi, Jun, Shimomoto, Kazuma
The aim of this article is to investigate interrelated structures lying among three notable problems in commutative algebra. These are Lifting problem, Ascent/descent along associated graded rings, and Matijevic-Roberts type problem.
Comment: Co
Comment: Co
Externí odkaz:
http://arxiv.org/abs/2312.05477
Autor:
Ishizuka, Ryo, Shimomoto, Kazuma
Over a complete Noetherian local domain of mixed characteristic with perfect residue field, we construct a perfectoid ring which is similar to an explicit representation of a perfect closure in positive characteristic. Then we demonstrate that this p
Externí odkaz:
http://arxiv.org/abs/2303.13872
The purpose of this note is to relate certain ring-theoretic properties of rings in mixed and positive characteristics that are related to each other by a tilting operation used in perfectoid geometry. To this aim, we exploit the multiplicative struc
Externí odkaz:
http://arxiv.org/abs/2301.01765
To initiate a systematic study on the applications of perfectoid methods to Noetherian rings, we introduce the notions of perfectoid towers and their tilts. We mainly show that the tilting operation preserves several homological invariants and finite
Externí odkaz:
http://arxiv.org/abs/2203.16400
Autor:
Shimomoto, Kazuma, Tavanfar, Ehsan
Publikováno v:
J. Algebra, 634 (2023) 667-697
We show that any quasi-Gorenstein deformation of a $3$-dimensional quasi-Gorenstein Buchsbaum local ring with $I$-invariant $1$ admits a maximal Cohen-Macaulay module, provided it is a quotient of a Gorenstein ring. Such a class of rings includes two
Externí odkaz:
http://arxiv.org/abs/2203.10368
Autor:
Shimomoto, Kazuma, Tavanfar, Ehsan
For any $d\ge 4$, by deformation theory of schemes, we present examples of (complete or excellent) $d$-dimensional mixed characteristic normal local domains admitting no small Cohen-Macaulay algebra, but admitting instances of small (maximal) Cohen-M
Externí odkaz:
http://arxiv.org/abs/2109.12700
The second vanishing theorem has a long history in the theory of local cohomology modules, which connects the vanishing of a complete regular local ring with a topological property of the punctured spectrum of the ring under some conditions. However,
Externí odkaz:
http://arxiv.org/abs/2107.09041
Autor:
Ishiro, Shinnosuke, Shimomoto, Kazuma
The almost purity theorem is central to the geometry of perfectoid spaces and has numerous applications in algebra and geometry. This result is known to have several different proofs in the case that the base ring is a perfectoid valuation ring. We g
Externí odkaz:
http://arxiv.org/abs/2012.13984
Autor:
Horiuchi, Jun, Shimomoto, Kazuma
In this article, we give a few examples of local rings in relation to weak normality and seminormality in mixed characteristic. It is known that two concepts can differ in the equal prime characteristic case, while they coincide in the equal characte
Externí odkaz:
http://arxiv.org/abs/2004.12017