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| 049 | _aMAIN | ||
| 100 | 1 |
_aHrushovski, Ehud, _d1959- _eauthor. _964664 |
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| 245 | 1 | 0 |
_aNon-archimedean tame topology and stably dominated types / _cEhud Hrushovski, Fran�cois Loeser. |
| 264 | 1 |
_aPrinceton : _bPrinceton University Press, _c2016. |
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| 264 | 4 | _c�2016 | |
| 300 | _a1 online resource (vii, 216 pages) | ||
| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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| 490 | 1 |
_aAnnals of mathematics studies ; _vnumber 192 |
|
| 504 | _aIncludes bibliographical references (pages 207-210) and index. | ||
| 588 | 0 | _aVendor-supplied metadata. | |
| 520 | _aOver the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural tools. For non-archimedean fields, such as the p-adics, the Berkovich analytification provides a connected topology with many thoroughgoing analogies to the real topology on the set of complex points, and it has become an important tool in algebraic dynamics and many other areas of geometry. This book lays down model-theoretic foundations for non-archimedean geometry. The methods combine o-minimality and stability theory. Definable types play a central role, serving first to define the notion of a point and then properties such as definable compactness. Beyond the foundations, the main theorem constructs a deformation retraction from the full non-archimedean space of an algebraic variety to a rational polytope. This generalizes previous results of V. Berkovich, who used resolution of singularities methods. No previous knowledge of non-archimedean geometry is assumed. Model-theoretic prerequisites are reviewed in the first sections. | ||
| 546 | _aIn English. | ||
| 505 | 0 | 0 |
_6880-01 _tFrontmatter -- _tContents -- _t1. Introduction -- _t2. Preliminaries -- _t3. The space �v of stably dominated types -- _t4. Definable compactness -- _t5. A closer look at the stable completion -- _t6. [Gamma]-internal spaces -- _t7. Curves -- _t8. Strongly stably dominated points -- _t9. Specializations and ACV2F -- _t10. Continuity of homotopies -- _t11. The main theorem -- _t12. The smooth case -- _t13. An equivalence of categories -- _t14. Applications to the topology of Berkovich spaces -- _tBibliography -- _tIndex -- _tList of notations. |
| 590 |
_aIEEE _bIEEE Xplore Princeton University Press eBooks Library |
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| 650 | 0 |
_aTame algebras. _964665 |
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| 650 | 6 |
_aAlg�ebres r�eguli�eres. _964666 |
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| 650 | 7 |
_aMATHEMATICS _xAlgebra _xIntermediate. _2bisacsh _964159 |
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| 650 | 7 |
_aMATHEMATICS _xTopology. _2bisacsh _914301 |
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| 650 | 7 |
_aTame algebras. _2fast _0(OCoLC)fst01142421 _964665 |
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| 655 | 0 |
_aElectronic book. _97794 |
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_aElectronic books. _93294 |
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_aElectronic books. _2lcgft _93294 |
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| 700 | 1 |
_aLoeser, Fran�cois, _eauthor. _964667 |
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| 776 | 0 | 8 |
_iPrint version: _z9780691161686 |
| 830 | 0 |
_aAnnals of mathematics studies ; _vno. 192. _964668 |
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| 856 | 4 | 0 | _uhttps://ieeexplore.ieee.org/servlet/opac?bknumber=9452405 |
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_6505-01/(S _tFrontmatter -- _tContents -- _t1. Introduction -- _t2. Preliminaries -- _t3. The space �v of stably dominated types -- _t4. Definable compactness -- _t5. A closer look at the stable completion -- _t6. (SD(B-internal spaces -- _t7. Curves -- _t8. Strongly stably dominated points -- _t9. Specializations and ACV2F -- _t10. Continuity of homotopies -- _t11. The main theorem -- _t12. The smooth case -- _t13. An equivalence of categories -- _t14. Applications to the topology of Berkovich spaces -- _tBibliography -- _tIndex -- _tList of notations. |
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