60 research outputs found
Norm1ToriHNP for GAP 4 ver.2025.07.18
No full textThis code provides algorithms related to computations of total obstruction to the Hasse norm principle
Noether's problem and rationality problem for multiplicative invariant fields: a survey (Algebraic Number Theory and Related Topics 2016)
Get PDF"Algebraic Number Theory and Related Topics 2016". November 28 - December 2, 2016. edited by Yasuo Ohno, Hiroshi Tsunogai and Toshiro Hiranouchi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.In this paper, we give a brief survey of recent developments on Noether's problem and rationality problem for multiplicative invariant fields including author's recent papers Hoshi [Hos15] about Noether's problem over Q, Hoshi, Kang and Kunyavskii [HKK13], Chu, Hoshi, Hu and Kang [CHHK15], Hoshi [Hos16] and Hoshi, Kang and Yamasaki [HKY16] about Noether's problem over C, and Hoshi, Kang and Kitayama [HKK14] and Hoshi, Kang and Yamasaki [HKY] about rationality problem for multiplicative invariant fields
Rationality problem for quasi-monomial actions (Algebraic Number Theory and Related Topics 2012)
Get PDF"Algebraic Number Theory and Related Topics 2012". December 3～7, 2012. edited by Atsushi Shiho, Tadashi Ochiai and Noriyuki Otsubo. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.We give a short survey of the rationality problem for quasi-monomial actions which includes Noether s problem and the rationality problem for algebraic tori, and report some results on rationality problem in three recent papers Hoshi, Kang and Kitayama [HKKi], Hoshi, Kang and Kunyavskii [HKKu] and Hoshi and Yamasaki [HY]
Rationality problem of two-dimensional quasi-monomial group actions
Get PDFThe rationality problem of two-dimensional purely quasi-monomial actions was
solved completely by Hoshi, Kang and Kitayama [HKK]. As a generalization, we
solve the rationality problem of two-dimensional quasi-monomial actions under
the condition that the actions are defined within the base field. In order to
prove the theorem, we give a brief review of the Severi-Brauer variety with
some examples and rationality results. We also use a rationality criterion for
conic bundles of over non-closed fields.Comment: To appear in Transformation Groups, 29 pages. Theorem 1.6 is
improved. Remark 1.7 is added. Theorem 2.7 is deleted. Section 3 (Proof of
Theorem 1.6) is greatly improved by referee's valuable suggestions. Remarks
3.1, 3.2, 3.3, 3.4 are added. Some typos are correcte
ソスウ イスウ ノ ジュンカイグン ニ タイスル ネーター モンダイ ニツイテ ケイサン ダイスウ システム ニヨル アタラシイ スウガク ノ カイタク ト シンテン
No full text有理数体mathbb{Q}上の素数位数の巡回群Cpに対するネーター問題は, mathbb{Q}上の有理関数体mathbb{Q}(x_{1}, ldots, x_{p})への巡回群Cpの変数の置換による作用の不変体mathbb{Q}(x_{1}, ldots, x_{p})^{C_{p}}={ain mathbb{Q}(x_{1}, ldots, x_{p})|(a)=a(forall in C_{p})}がmathbb{Q}上有理的(純超越的)か?を問うており, 17個の素数pleq43とp=61, 67, 71に対して肯定解をもつことが知られているが, 解が肯定的となる素数pが無限に存在するかどうかは分かっていない. 本稿では, 既知の結果の概説を行うとともに, 論文[Hos15]における, PARI/GPによるp<20000なる素数pに対する計算結果を紹介する
Birational classification for algebraic tori
Get PDF於 京都大学理学研究科セミナーハウス (2024年10月22日-10月25日)2024年度科学研究費補助金 基盤研究(A)(課題番号 20H00111, 代表 小木曽啓示)2024年度科学研究費補助金 基盤研究(A)(課題番号 21H04429, 代表 並河良典)Date : October 22nd - 25th, 2024Location: Kyoto University (North Campus), Science Seminar HouseJSPS KAKENHI Grant-in-Aid (A) 20H00111 (Keiji Oguiso)JSPS KAKENHI Grant-in-Aid (A) 21H04429 (Yoshinori Namikawa)Organizers: Yohsuke Matsuzawa, Yusuke Nakamura, Kazuhiko YamakiWe give a stably birational classification for algebraic -tori of dimensions 3 and 4 over a field . Kunyavskii [Kun90] proved that there exist 15 not stably -rational cases among 73 cases of algebraic -tori of dimension 3. Hoshi and Yamasaki [HY17] showed that there exist exactly 487 (resp. 7, resp. 216) stably -rational (resp. not stably but retract -rational, resp. not retract -rational) cases of algebraic -tori of dimension 4. First, we define the weak stably -equivalence of algebraic -tori and show that there exist 13 (resp. 128) weak stably -equivalent classes of algebraic -tori T of dimension 3 (resp. 4) which are not stably -rational by computing some cohomological stably birational invariants, e.g. the Brauer-Grothendieck group of where is a smooth -compactification of , provided by Kunyavskii, Skorobogatov and Tsfasman [KST89]. We make a procedure to compute such stably birational invariants effectively and the computations are done by using the computer algebra system GAP. Second, we define the -part of the flabby class [[T]]ᶠˡ as a ℤₚ[ₚ()]-lattice and prove that they are faithful and indecomposable ℤₚ[ₚ()]-lattices unless it vanishes for = 2 (resp. = 2, 3) in dimension 3 (resp. 4). The ℤₚ-ranks of them are also given. Third, we give a necessary and sufficient condition for which two not stably -rational algebraic k-tori and ′ of dimensions 3 (resp. 4) are stably birationally -equivalent in terms of the splitting fields and the weak stably -equivalent classes of and ′. In particular, the splitting fields of them should coincide if [T] and [T]′ are indecomposable. Forth, for each 7 cases of not stably but retract -rational algebraic -tori of dimension 4, we find an algebraic -torus ′ of dimension 4 which satisfies that ×[]′ is stably -rational. Finally, we give a criteria to determine whether two algebraic -tori and ′ of general dimensions are stably birationally -equivalent when (resp. ′) is stably birationally -equivalent to some algebraic -torus T″ of dimension up to 4. This is a joint work with Aiichi Yamasaki (arXiv: 2112.02280)
“Literatura de Fantasma” no Japão: A construção do insólito em contos da chuva e da lua de Ueda Akinari.
No full textUeda Akinari (1734-1809) é considerado por sua obra Contos da chuva e da lua (Ugetsu Monogatari, 1776) o mais aclamado autor japonês de contos com temática do insólito. O presente artigo tem como objetivo analisar os contos “Buppôsô” e “Pacto do crisântemo” presentes nessa obra, buscando compreendê-los a partir das teorizações consagradas sobre o gênero, bem como propor uma discussão acerca de alguns desses conceitos relacionando-os com as especificidades da literatura insólita japonesa.Ueda Akinari (1734-1809) is considered by his work Tales of moonlight and rain (Ugetsu Monogatari, 1776) the most acclaimed Japanese author of short stories with themes of the unusual. This paper aims to analyze the stories “The Owl of the Three Jewels” and “Chrysanthemum Vow” present in this work, seeking to understand them from classical theories about gender, and propose a discussion of some of these concepts by relating them Japanese unusual literature characteristics
Norm one tori and Hasse norm principle, II: Degree case
Get PDFLet be a field, be an algebraic -torus, be a smooth
-compactification of and be the Picard group
of . Hoshi, Kanai and Yamasaki [HKY22]
determined for norm one tori
and gave a necessary and sufficient condition for the
Hasse norm principle for extensions of number fields with and . In this paper, we determine cases with and give a necessary and sufficient condition for
the Hasse norm principle for where .Comment: To appear in J. Number Theory, 148 page
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