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An explicit self-dual construction of complete cotorsion pairs in the relative context 完备扭转对的显式自对偶构造
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2020-06-02 DOI: 10.4171/RSMUP/118
L. Positselski
{"title":"An explicit self-dual construction of complete cotorsion pairs in the relative context","authors":"L. Positselski","doi":"10.4171/RSMUP/118","DOIUrl":"https://doi.org/10.4171/RSMUP/118","url":null,"abstract":"Let $Rto A$ be a homomorphism of associative rings, and let $(mathcal F,mathcal C)$ be a hereditary complete cotorsion pair in $Rmathsf{-Mod}$. Let $(mathcal F_A,mathcal C_A)$ be the cotorsion pair in $Amathsf{-Mod}$ in which $mathcal F_A$ is the class of all left $A$-modules whose underlying $R$-modules belong to $mathcal F$. Assuming that the $mathcal F$-resolution dimension of every left $R$-module is finite and the class $mathcal F$ is preserved by the coinduction functor $operatorname{Hom}_R(A,-)$, we show that $mathcal C_A$ is the class of all direct summands of left $A$-modules finitely filtered by $A$-modules coinduced from $R$-modules from $mathcal C$. Assuming that the class $mathcal F$ is closed under countable products and preserved by the functor $operatorname{Hom}_R(A,-)$, we prove that $mathcal C_A$ is the class of all direct summands of left $A$-modules cofiltered by $A$-modules coinduced from $R$-modules from $mathcal C$, with the decreasing filtration indexed by the natural numbers. A combined result, based on the assumption that countable products of modules from $mathcal F$ have finite $mathcal F$-resolution dimension bounded by $k$, involves cofiltrations indexed by the ordinal $omega+k$. The dual results also hold, provable by the same technique going back to the author's monograph on semi-infinite homological algebra arXiv:0708.3398. In addition, we discuss the $n$-cotilting and $n$-tilting cotorsion pairs, for which we obtain better results using a suitable version of the classical Bongartz lemma. As an illustration of the main results of the paper, we consider certain cotorsion pairs related to the contraderived and coderived categories of curved DG-modules.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85124162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
The flatness of ternary cyclotomic polynomials 三元环多项式的平坦性
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2020-05-26 DOI: 10.4171/rsmup/47
Bin Zhang
{"title":"The flatness of ternary cyclotomic polynomials","authors":"Bin Zhang","doi":"10.4171/rsmup/47","DOIUrl":"https://doi.org/10.4171/rsmup/47","url":null,"abstract":"It is well known that all of the prime cyclotomic polynomials and binary cyclotomic polynomials are flat, and the flatness of ternary cyclotomic polynomials is much more complicated. Let p < q < r be odd primes such that zr ≡ ±1 (mod pq), where z is a positive integer. So far, the classification of flat ternary cyclotomic polynomials for 1 ≤ z ≤ 5 has been given. In this paper, for z = 6 and q ≡ ±1 (mod p), we give the necessary and sufficient conditions for ternary cyclotomic polynomials Φpqr(x) to be flat. Mathematics Subject Classification (2010). 11B83, 11C08, 11N56.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"463 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75124336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A monodromy criterion for the good reduction of $K3$ surfaces K3曲面良好约化的单一性判据
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2020-05-25 DOI: 10.4171/rsmup/50
Genaro Hernandez-Mada
{"title":"A monodromy criterion for the good reduction of $K3$ surfaces","authors":"Genaro Hernandez-Mada","doi":"10.4171/rsmup/50","DOIUrl":"https://doi.org/10.4171/rsmup/50","url":null,"abstract":"We give a criterion for the good reduction of semistable K3 surfaces over p-adic fields. We use neither p-adic Hodge theory nor transcendental methods as in the analogous proofs of criteria for good reduction of curves or K3 surfaces. We achieve our goal by realizing the special fiber Xs of a semistable model X of a K3 surface over the p-adic field K, as a special fiber of a log-family in characteristic p and use an arithmetic version of the Clemens-Schmid exact sequence in order to obtain a Kulikov-Persson-Pinkham classification theorem in characteristic p. Mathematics Subject Classification (2010). 14F30, 11G25, 14F35","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79051361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Closed ideals in the uniform topology on the ring of real-valued continuous functions on a frame 系上实值连续函数环上一致拓扑的闭理想
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2020-05-24 DOI: 10.4171/rsmup/43
M. Abedi, A. Estaji
{"title":"Closed ideals in the uniform topology on the ring of real-valued continuous functions on a frame","authors":"M. Abedi, A. Estaji","doi":"10.4171/rsmup/43","DOIUrl":"https://doi.org/10.4171/rsmup/43","url":null,"abstract":"For a completely regular frame L, the ring RL of real-valued continuous functions on L is equipped with the uniform topology. The closed ideals of RL in this topology are studied, and a new, merely algebraic characterization of these ideals is given. This result is used to describe the real ideals of RL, and to characterize pseudocompact frames and Lindelöf frames. It is shown that a frame L is finite if and only if every ideal of RL is closed. Finally, we prove that every closed ideal in RL is an intersection of maximal ideals. Mathematics Subject Classification (2010). Primary: 06D22; Secondary: 54C40, 54C50, 16D25, 13J20.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"15 1","pages":"135-152"},"PeriodicalIF":0.0,"publicationDate":"2020-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89328385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Milnor’s alternative for finitely generated relatively free groups that are locally graded Milnor对于有限生成的相对自由的局部分级群体的替代方案
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2020-05-24 DOI: 10.4171/rsmup/46
W. Hołubowski, O. Macedońska
{"title":"Milnor’s alternative for finitely generated relatively free groups that are locally graded","authors":"W. Hołubowski, O. Macedońska","doi":"10.4171/rsmup/46","DOIUrl":"https://doi.org/10.4171/rsmup/46","url":null,"abstract":"Let G be a finitely generated relatively free group that is locally graded. We show that either G contains a non-trivial free subsemigroup or G is nilpotent-by-finite.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"73 1","pages":"247-250"},"PeriodicalIF":0.0,"publicationDate":"2020-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84299300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A notion analogous to the discriminant for transcendental elements in certain extensions of local fields 一种类似于局部域的某些扩展中超越元素的判别式的概念
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2020-05-24 DOI: 10.4171/rsmup/41
S. Achimescu, V. Alexandru, C. S. Andronescu
{"title":"A notion analogous to the discriminant for transcendental elements in certain extensions of local fields","authors":"S. Achimescu, V. Alexandru, C. S. Andronescu","doi":"10.4171/rsmup/41","DOIUrl":"https://doi.org/10.4171/rsmup/41","url":null,"abstract":"Let (K, |·|) be a local field. In this paper we define an invariant analogous to the discriminant over K for certain transcendental elements over K. Mathematics Subject Classification (2010). Primary: 11S99; Secondary: 13A18, 12J05, 12J10, 12J25.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"8 1","pages":"105-112"},"PeriodicalIF":0.0,"publicationDate":"2020-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86301991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sign-changing solutions of boundary value problems for semilinear $Delta_{gamma}$-Laplace equations 半线性$Delta_{gamma}$ -拉普拉斯方程边值问题的变符号解
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2020-05-24 DOI: 10.4171/rsmup/42
D. T. Luyen
{"title":"Sign-changing solutions of boundary value problems for semilinear $Delta_{gamma}$-Laplace equations","authors":"D. T. Luyen","doi":"10.4171/rsmup/42","DOIUrl":"https://doi.org/10.4171/rsmup/42","url":null,"abstract":"","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"16 1","pages":"113-134"},"PeriodicalIF":0.0,"publicationDate":"2020-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73319214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Divisibility and duo-rings 可整除性和双环
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2020-05-24 DOI: 10.4171/rsmup/40
U. Albrecht, Bradley McQuaig
{"title":"Divisibility and duo-rings","authors":"U. Albrecht, Bradley McQuaig","doi":"10.4171/rsmup/40","DOIUrl":"https://doi.org/10.4171/rsmup/40","url":null,"abstract":"This paper investigates the projective dimension of the maximal right ring of quotients Q(R) of a right non-singular ring R. Our discussion addresses the question under which conditions p.d.(Q)) ≤ 1 guarantees that the module Q/R is a direct sum of countably generated modules extending Matlis’ Theorem for integral domains to a non-commutative setting. Mathematics Subject Classification (2010). Primary: 16D10; Secondary: 16D40, 16E30, 16P50, 16P60, 16S85.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"90 1","pages":"81-103"},"PeriodicalIF":0.0,"publicationDate":"2020-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77874172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Note on algebraic irregular Riemann–Hilbert correspondence 代数不规则黎曼-希尔伯特对应的注释
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2020-04-26 DOI: 10.4171/rsmup/119
Yohei Ito
{"title":"Note on algebraic irregular Riemann–Hilbert correspondence","authors":"Yohei Ito","doi":"10.4171/rsmup/119","DOIUrl":"https://doi.org/10.4171/rsmup/119","url":null,"abstract":"The subject of this paper is an algebraic version of the irregular Riemann-Hilbert correspondence which was mentioned in [arXiv:1910.09954] by the author. In particular, we prove an equivalence of categories between the triangulated category of algebraic holonomic D-modules on a smooth algebraic variety and the one of algebraic C-constructible enhanced ind-sheaves. Moreover we show that there exists a t-structure on the triangulated category of algebraic C-constructible enhanced ind-sheaves whose heart is equivalent to the abelian category of algebraic holonomic D-modules. Furthermore we shall consider simple objects of its heart and minimal extensions of objects of its heart.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85848475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Convolution identities of poly-Cauchy numbers with level 2 二阶多柯西数的卷积恒等式
Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2020-03-29 DOI: 10.4171/rsmup/106
T. Komatsu
{"title":"Convolution identities of poly-Cauchy numbers with level 2","authors":"T. Komatsu","doi":"10.4171/rsmup/106","DOIUrl":"https://doi.org/10.4171/rsmup/106","url":null,"abstract":"Poly-Cauchy numbers with level $2$ are defined by inverse sine hyperbolic functions with the inverse relation from sine hyperbolic functions. In this paper, we show several convolution identities of poly-Cauchy numbers with level $2$. In particular, that of three poly-Cauchy numbers with level $2$ can be expressed as a simple form. In the sequel, we introduce the Stirling numbers of the first kind with level $2$","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76566254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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