Algebraic Geometry and Arithmetic Curves / (Record no. 2795)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 02003 a2200181 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9780199202492 (pbk.) |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 516.35 LIU |
| 100 ## - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Liu, Qing |
| 245 ## - TITLE STATEMENT | |
| Title | Algebraic Geometry and Arithmetic Curves / |
| Statement of responsibility, etc | Qing Liu |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Name of publisher | OUP, |
| Place of publication | New York: |
| Year of publication | c2002. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | xv, 577p. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Includes Bibliography (557- 561) & Index (562-577). |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem) This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularization (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the fundamental theorem of stable reduction of Deligne-Mumford. This book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are few, and including many examples and approximately 600 exercises, the book is ideal for graduate students. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Curves, Algebraic |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Arithmetical algebraic geometry |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Geometry, Algebraic |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | Books |
| Withdrawn status | Lost status | Damaged status | Not for loan | Permanent Location | Current Location | Shelving location | Date acquired | Source of acquisition | Cost, normal purchase price | Full call number | Accession Number | Cost, replacement price | Price effective from | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Vigyanpuri Campus | Vigyanpuri Campus | Mathematics | 01/10/2022 | 14 | 3882.70 | 516.35 LIU | 005478 | 11514.00 | 01/10/2022 | Course Reserve | ||||
| Vigyanpuri Campus | Vigyanpuri Campus | Mathematics | 01/10/2022 | 14 | 3882.70 | 516.35 LIU | 005480 | 11514.00 | 01/10/2022 | Books | ||||
| Vigyanpuri Campus | Vigyanpuri Campus | Mathematics | 01/10/2022 | 14 | 3882.70 | 516.35 LIU | 005479 | 11514.00 | 01/10/2022 | Books |