Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.jalgebra.2023.06.045

Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Cambridge University Press (CUP)  

Abstract

In this article, we prove that a complete Noetherian local domain of mixed characteristic $p>0$ with perfect residue field has an integral extension that is an integrally closed, almost Cohen–Macaulay domain such that the Frobenius map is surjective modulo p. This result is seen as a mixed characteristic analog of the fact that the perfect closure of a complete local domain in positive characteristic is almost Cohen–Macaulay. To this aim, we carry out a detailed study of decompletion of perfectoid rings and establish the Witt-perfect (decompleted) version of André’s perfectoid Abhyankar’s lemma and Riemann’s extension theorem.

DOI： 10.1017/nmj.2023.23

Authorship：Corresponding author   Language：English  

Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

ネーター局所整域で混合標数を持つ場合に弱正規性や半正規性の性質や具体例を調べた。またBertini型定理を証明した。

DOI： 10.1216/jca.2022.14.351

Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.jpaa.2021.106898

Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1215/21562261-2021-0011

Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.jalgebra.2020.06.032

Scopus

Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

ネーター局所環を係数に持つオイラー形式の議論を一般化することに成功した。またこれらの結果を用いて、概通常なp-進モジュラー形式に伴う正規な概通常肥田ヘッケ環に付随する岩澤主予想を部分的に解決した。

DOI： 10.1007/s40316-018-0099-0

Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

混合標数を持つ離散付値環上定義された正規な射影スキームが十分に沢山の正規なCartier因子を持つことを示した。応用として正規スキームの因子類群に関する結果を得た。

DOI： 10.1080/00927872.2018.1470244

Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

完備局所環に関するCohenの構造定理がGabberによって改良された。この論文ではCohen-Gabberの定理に対して初等的な別証明を与えた。

DOI： 10.2748/tmj/1537495352

Authorship：Last author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Wiley  

In this paper we study the local cohomology modules of Du Bois singularities. Let $(R,\mathfrak{m})$ be a local ring; we prove that if $R_{\text{red } }$ is Du Bois, then $H_{\mathfrak{m } }^{i}(R)\rightarrow H_{\mathfrak{m } }^{i}(R_{\text{red } })$ is surjective for every $i$. We find many applications of this result. For example, we answer a question of Kovács and Schwede [Inversion of adjunction for rational and Du Bois pairs, Algebra Number Theory 10 (2016), 969–1000; MR 3531359] on the Cohen–Macaulay property of Du Bois singularities. We obtain results on the injectivity of $\operatorname{Ext}$ that provide substantial partial answers to questions in Eisenbud et al. [Cohomology on toric varieties and local cohomology with monomial supports, J. Symbolic Comput. 29 (2000), 583–600] in characteristic $0$. These results can also be viewed as generalizations of the Kodaira vanishing theorem for Cohen–Macaulay Du Bois varieties. We prove results on the set-theoretic Cohen–Macaulayness of the defining ideal of Du Bois singularities, which are characteristic-$0$ analogs and generalizations of results of Singh–Walther and answer some of their questions in Singh and Walther [On the arithmetic rank of certain Segre products, in Commutative algebra and algebraic geometry, Contemporary Mathematics, vol. 390 (American Mathematical Society, Providence, RI, 2005), 147–155]. We extend results on the relation between Koszul cohomology and local cohomology for $F$-injective and Du Bois singularities first shown in Hochster and Roberts [The purity of the Frobenius and local cohomology, Adv. Math. 21 (1976), 117–172; MR 0417172 (54 #5230)]. We also prove that singularities of dense $F$-injective type deform.

DOI： 10.1112/s0010437x17007321

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.aim.2017.04.002

Web of Science

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1080/00927872.2016.1175575

Web of Science

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.jpaa.2015.07.008

Web of Science

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1215/00277630-2891620

Web of Science

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1080/00927872.2014.974259

Web of Science

Language：English   Publishing type：Research paper (scientific journal)  

Web of Science

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1216/JCA-2012-4-4-445

Scopus

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.jalgebra.2011.05.006

Web of Science

Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

Fontaineによるp進周期環の構成を真似て、混合標数を持つ完備局所環が弱い意味でのAlmost Cohen-Macaulay環を持つことを証明した。

DOI： 10.1215/ijm/1355927030

Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.jpaa.2008.11.047

Web of Science

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1112/S0010437X07002825

Web of Science

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.jalgebra.2004.11.014

Web of Science

Event date： 2023.12

Language：English   Presentation type：Oral presentation (general)  

Event date： 2021.9

Language：Japanese   Presentation type：Oral presentation (invited, special)  

Language：English   Presentation type：Oral presentation (invited, special)  

Venue：West Virginia University  

Language：English   Presentation type：Symposium, workshop panel (nominated)  

Venue：Ton Duc Thang University(ベトナム，ホーチミン)  

Language：English   Presentation type：Oral presentation (invited, special)  

Venue：University Minnesota  

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：首都大学東京  

Language：English   Presentation type：Symposium, workshop panel (nominated)  

Venue：IPC(神奈川県葉山市)  

Language：English   Presentation type：Symposium, workshop panel (nominated)  

Venue：明治大学  

Language：Japanese   Presentation type：Symposium, workshop panel (nominated)  

Venue：佐賀大学  

Language：English   Presentation type：Oral presentation (invited, special)  

Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Venue：東京大学数理科学研究科棟123号室  

Language：English   Presentation type：Symposium, workshop panel (nominated)  

Venue：京都大学数理解析研究所（京都府京都市)  

Language：English   Presentation type：Oral presentation (invited, special)  

Venue：Zoom   Country：Iran, Islamic Republic of  

Language：Japanese   Presentation type：Symposium, workshop panel (public)  

Language：English   Presentation type：Oral presentation (general)  

Venue：Virtual  

Language：English   Presentation type：Oral presentation (general)  

Venue：Virtual   Country：India  

Language：English   Presentation type：Oral presentation (general)  

Venue：倉敷シーサイドホテル  

Language：English   Presentation type：Oral presentation (general)  

Venue：倉敷シーサイドホテル