Local Analytic Geometry: Basic Theory and Applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Wiesbaden
Vieweg+Teubner Verlag
2000
|
| Schriftenreihe: | Advanced Lectures in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Algebraic geometry is, loosely speaking, concerned with the study of zero sets of polynomials (over an algebraically closed field). As one often reads in prefaces of int- ductory books on algebraic geometry, it is not so easy to develop the basics of algebraic geometry without a proper knowledge of commutative algebra. On the other hand, the commutative algebra one needs is quite difficult to understand without the geometric motivation from which it has often developed. Local analytic geometry is concerned with germs of zero sets of analytic functions, that is, the study of such sets in the neighborhood of a point. It is not too big a surprise that the basic theory of local analytic geometry is, in many respects, similar to the basic theory of algebraic geometry. It would, therefore, appear to be a sensible idea to develop the two theories simultaneously. This, in fact, is not what we will do in this book, as the "commutative algebra" one needs in local analytic geometry is somewhat more difficult: one has to cope with convergence questions. The most prominent and important example is the substitution of division with remainder. Its substitution in local analytic geometry is called the Weierstraft Division Theorem. The above remarks motivated us to organize the first four chapters of this book as follows. In Chapter 1 we discuss the algebra we need. Here, we assume the reader attended courses on linear algebra and abstract algebra, including some Galois theory |
| Beschreibung: | 1 Online-Ressource (XI, 384 p) |
| ISBN: | 9783322901590 9783528031374 |
| ISSN: | 0932-7134 |
| DOI: | 10.1007/978-3-322-90159-0 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-322-90159-0 |
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| isbn | 9783322901590 9783528031374 |
| issn | 0932-7134 |
| language | English |
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| spelling | Jong, Theo Verfasser aut Local Analytic Geometry Basic Theory and Applications by Theo Jong, Gerhard Pfister Wiesbaden Vieweg+Teubner Verlag 2000 1 Online-Ressource (XI, 384 p) txt rdacontent c rdamedia cr rdacarrier Advanced Lectures in Mathematics 0932-7134 Algebraic geometry is, loosely speaking, concerned with the study of zero sets of polynomials (over an algebraically closed field). As one often reads in prefaces of int- ductory books on algebraic geometry, it is not so easy to develop the basics of algebraic geometry without a proper knowledge of commutative algebra. On the other hand, the commutative algebra one needs is quite difficult to understand without the geometric motivation from which it has often developed. Local analytic geometry is concerned with germs of zero sets of analytic functions, that is, the study of such sets in the neighborhood of a point. It is not too big a surprise that the basic theory of local analytic geometry is, in many respects, similar to the basic theory of algebraic geometry. It would, therefore, appear to be a sensible idea to develop the two theories simultaneously. This, in fact, is not what we will do in this book, as the "commutative algebra" one needs in local analytic geometry is somewhat more difficult: one has to cope with convergence questions. The most prominent and important example is the substitution of division with remainder. Its substitution in local analytic geometry is called the Weierstraft Division Theorem. The above remarks motivated us to organize the first four chapters of this book as follows. In Chapter 1 we discuss the algebra we need. Here, we assume the reader attended courses on linear algebra and abstract algebra, including some Galois theory Mathematics Geometry Mathematics, general Mathematik Analytische Geometrie (DE-588)4001867-2 gnd rswk-swf Lokale analytische Geometrie (DE-588)4593932-9 gnd rswk-swf Analytische Geometrie (DE-588)4001867-2 s 1\p DE-604 Lokale analytische Geometrie (DE-588)4593932-9 s 2\p DE-604 Pfister, Gerhard Sonstige oth https://doi.org/10.1007/978-3-322-90159-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jong, Theo Local Analytic Geometry Basic Theory and Applications Mathematics Geometry Mathematics, general Mathematik Analytische Geometrie (DE-588)4001867-2 gnd Lokale analytische Geometrie (DE-588)4593932-9 gnd |
| subject_GND | (DE-588)4001867-2 (DE-588)4593932-9 |
| title | Local Analytic Geometry Basic Theory and Applications |
| title_auth | Local Analytic Geometry Basic Theory and Applications |
| title_exact_search | Local Analytic Geometry Basic Theory and Applications |
| title_full | Local Analytic Geometry Basic Theory and Applications by Theo Jong, Gerhard Pfister |
| title_fullStr | Local Analytic Geometry Basic Theory and Applications by Theo Jong, Gerhard Pfister |
| title_full_unstemmed | Local Analytic Geometry Basic Theory and Applications by Theo Jong, Gerhard Pfister |
| title_short | Local Analytic Geometry |
| title_sort | local analytic geometry basic theory and applications |
| title_sub | Basic Theory and Applications |
| topic | Mathematics Geometry Mathematics, general Mathematik Analytische Geometrie (DE-588)4001867-2 gnd Lokale analytische Geometrie (DE-588)4593932-9 gnd |
| topic_facet | Mathematics Geometry Mathematics, general Mathematik Analytische Geometrie Lokale analytische Geometrie |
| url | https://doi.org/10.1007/978-3-322-90159-0 |
| work_keys_str_mv | AT jongtheo localanalyticgeometrybasictheoryandapplications AT pfistergerhard localanalyticgeometrybasictheoryandapplications |