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pro vyhledávání: '"Datta, Rankeya"'
Let $S$ be a submonoid of a free Abelian group of finite rank. We show that if $k$ is a field of prime characteristic such that the monoid $k$-algebra $k[S]$ is split $F$-regular, then $k[S]$ is a finitely generated $k$-algebra, or equivalently, that
Externí odkaz:
http://arxiv.org/abs/2402.16974
We systematically study the intersection flatness and Ohm-Rush properties for modules over a commutative ring, drawing inspiration from the work of Ohm and Rush and of Hochster and Jeffries. We then use our newfound understanding of these properties
Externí odkaz:
http://arxiv.org/abs/2305.11139
Autor:
Datta, Rankeya, Tucker, Kevin
A splinter is a notion of singularity that has seen numerous recent applications, especially in connection with the direct summand theorem, the mixed characteristic minimal model program, Cohen-Macaulayness of absolute integral closures and cohomolog
Externí odkaz:
http://arxiv.org/abs/2103.10525
Autor:
Datta, Rankeya
Publikováno v:
Math. Nachr. 296 (2023), 1041-1055
Given a generically finite local extension of valuation rings $V \subset W$, the question of whether $W$ is the localization of a finitely generated $V$-algebra is significant for approaches to the problem of local uniformization of valuations using
Externí odkaz:
http://arxiv.org/abs/2101.08337
An $R$-algebra $S$ is $R$-solid if there exists a nonzero $R$-linear map $S \rightarrow R$. In characteristic $p$, the study of $F$-singularities such as Frobenius splittings implicitly rely on the $R$-solidity of $R^{1/p}$. Following recent results
Externí odkaz:
http://arxiv.org/abs/2007.10383
Autor:
Datta, Rankeya, Murayama, Takumi
Publikováno v:
J. Eur. Math. Soc. (JEMS) 25 (2023), no. 11, 4291-4314
An excellent ring of prime characteristic for which the Frobenius map is pure is also Frobenius split in many commonly occurring situations in positive characteristic commutative algebra and algebraic geometry. However, using a fundamental constructi
Externí odkaz:
http://arxiv.org/abs/2003.13714
Autor:
Antieau, Benjamin, Datta, Rankeya
We give three proofs that valuation rings are derived splinters: a geometric proof using the absolute integral closure, a homological proof which reduces the problem to checking that valuation rings are splinters (which is done in the second author's
Externí odkaz:
http://arxiv.org/abs/2002.01067
Autor:
Datta, Rankeya a, ⁎, Tucker, Kevin b
Publikováno v:
In Journal of Algebra 1 September 2023 629:307-357
Autor:
Datta, Rankeya, Tucker, Kevin
We show that Noetherian splinters ascend under essentially \'etale homomorphisms. Along the way, we also prove that the henselization of a Noetherian local splinter is always a splinter and that the completion of a local splinter with geometrically r
Externí odkaz:
http://arxiv.org/abs/1909.06891
Autor:
Datta, Rankeya, Simpson, Austyn
Let $k$ be an algebraically closed field of characteristic $p > 0$. We show that if $X\subseteq\mathbb{P}^n_k$ is an equidimensional subscheme with Hilbert--Kunz multiplicity less than $\lambda$ at all points $x\in X$, then for a general hyperplane $
Externí odkaz:
http://arxiv.org/abs/1908.04819