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Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems /
In this article the authors develop a new method to deal with maximal Cohen-Macaulay modules over non-isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen-Macaulay m...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2017.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1178. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 003 | OCoLC | ||
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| 019 | |a 1262690955 | ||
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| 049 | |a UAMI | ||
| 100 | 1 | |a Burban, Igor, |d 1977- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjKWWmVmhW8QhYRr8DD44q | |
| 245 | 1 | 0 | |a Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems / |c Igor Burban, Yuriy Drozd. |
| 264 | 1 | |a Providence, Rhode Island : |b American Mathematical Society, |c 2017. | |
| 264 | 4 | |c ©2017 | |
| 300 | |a 1 online resource (xiv, 114 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 0065-9266 ; |v volume 248, number 1178 | |
| 588 | 0 | |a Print version record. | |
| 500 | |a "Volume 248, number 1178 (fourth of 5 numbers), July 2017." | ||
| 504 | |a Includes bibliographical references (pages 111-114). | ||
| 505 | 0 | |a Cover; Title page; Introduction, motivation and historical remarks; Chapter 1. Generalities on maximal Cohen-Macaulay modules; 1.1. Maximal Cohen-Macaulay modules over surface singularities; 1.2. On the category \CM^{ }(\rA); Chapter 2. Category of triples in dimension one; Chapter 3. Main construction; Chapter 4. Serre quotients and proof of Main Theorem; Chapter 5. Singularities obtained by gluing cyclic quotient singularities; 5.1. Non-isolated surface singularities obtained by gluing normal rings; 5.2. Generalities about cyclic quotient singularities. | |
| 505 | 8 | |a 5.3. Degenerate cusps and their basic properties5.4. Irreducible degenerate cusps; 5.5. Other cases of degenerate cusps which are complete intersections; Chapter 6. Maximal Cohen-Macaulay modules over \kk\llbracket, \rrbracket/(²+ ³- ); Chapter 7. Representations of decorated bunches of chains-I; 7.1. Notation; 7.2. Bimodule problems; 7.3. Definition of a decorated bunch of chains; 7.4. Matrix description of the category \Rep(\dX); 7.5. Strings and Bands; 7.6. Idea of the proof; 7.7. Decorated Kronecker problem; Chapter 8. Maximal Cohen-Macaulay modules over degenerate cusps-I. | |
| 505 | 8 | |a 8.1. Maximal Cohen-Macaulay modules on cyclic quotient surface singularities8.2. Matrix problem for degenerate cusps; 8.3. Reconstruction procedure; 8.4. Cohen-Macaulay representation type and tameness of degenerate cusps; Chapter 9. Maximal Cohen-Macaulay modules over degenerate cusps-II; 9.1. Maximal Cohen-Macaulay modules over \kk\llbracket, \rrbracket/(); 9.2. Maximal Cohen-Macaulay modules over \kk\llbracket, \rrbracket/(,); 9.3. Degenerate cusp \kk\llbracket, \rrbracket/(,); Chapter 10. Schreyer's question. | |
| 505 | 8 | |a Chapter 11. Remarks on rings of discrete and tame CM-representation type11.1. Non-reduced curve singularities; 11.2. Maximal Cohen-Macaulay modules over the ring ̃ ((1,0)); 11.3. Other surface singularities of discrete and tame CM-representation type; 11.4. On deformations of certain non-isolated surface singularities; Chapter 12. Representations of decorated bunches of chains-II; 12.1. Decorated conjugation problem; 12.2. Some preparatory results from linear algebra; 12.3. Reduction to the decorated chessboard problem; 12.4. Reduction procedure for the decorated chessboard problem. | |
| 505 | 8 | |a 12.5. Indecomposable representations of a decorated chessboard12.6. Proof of the Classification Theorem; References; Back Cover. | |
| 520 | |a In this article the authors develop a new method to deal with maximal Cohen-Macaulay modules over non-isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen-Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen-Macaulay representation type. The authors' approach is illustrated on the case of \mathbb{k}[[x, y, z]]/(xyz) as well as several other rings. This study of maximal Cohen-Macaulay modules over non-isolated singulari. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Cohen-Macaulay modules. | |
| 650 | 0 | |a Modules (Algebra) | |
| 650 | 0 | |a Singularities (Mathematics) | |
| 650 | 0 | |a Matrices. | |
| 650 | 6 | |a Modules de Cohen-Macaulay. | |
| 650 | 6 | |a Modules (Algèbre) | |
| 650 | 6 | |a Singularités (Mathématiques) | |
| 650 | 6 | |a Matrices. | |
| 650 | 7 | |a Cohen-Macaulay modules |2 fast | |
| 650 | 7 | |a Matrices |2 fast | |
| 650 | 7 | |a Modules (Algebra) |2 fast | |
| 650 | 7 | |a Singularities (Mathematics) |2 fast | |
| 700 | 1 | |a Drozd, Yurij A., |e author. | |
| 710 | 2 | |a American Mathematical Society, |e publisher. | |
| 776 | 0 | 8 | |i Print version: |z 9781470425371 |w (DLC) 2017014982 |w (OCoLC)981907996 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1178. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=4940244 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH37445095 | ||
| 938 | |a EBL - Ebook Library |b EBLB |n EBL4940244 | ||
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