A conjecture of Ax and degenerations of Fano varieties

János Kollár

doi:10.1007/s11856-007-0097-4

A conjecture of Ax and degenerations of Fano varieties

János Kollár

Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

James Ax conjectured that every pseudo algebraically closed field is C ₁. We prove this conjecture in characteristic 0 by relating it to degenerations of Fano varieties.

Original language	English (US)
Pages (from-to)	235-251
Number of pages	17
Journal	Israel Journal of Mathematics
Volume	162
DOIs	https://doi.org/10.1007/s11856-007-0097-4
State	Published - Dec 2007

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11856-007-0097-4

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@article{e1bb0707760d48d5832469a8f1bfce97,

title = "A conjecture of Ax and degenerations of Fano varieties",

abstract = "James Ax conjectured that every pseudo algebraically closed field is C 1. We prove this conjecture in characteristic 0 by relating it to degenerations of Fano varieties.",

author = "J{\'a}nos Koll{\'a}r",

note = "Funding Information: Acknowledgements: I thank A. J. de Jong, H. Esnault, M. Jarden, J. McK-ernan, J. Starr and T. Szamuely for useful comments and suggestions. Partial financial support was provided by the NSF under grant number DMS-0500198.",

year = "2007",

month = dec,

doi = "10.1007/s11856-007-0097-4",

language = "English (US)",

volume = "162",

pages = "235--251",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

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AU - Kollár, János

N1 - Funding Information: Acknowledgements: I thank A. J. de Jong, H. Esnault, M. Jarden, J. McK-ernan, J. Starr and T. Szamuely for useful comments and suggestions. Partial financial support was provided by the NSF under grant number DMS-0500198.

PY - 2007/12

Y1 - 2007/12

N2 - James Ax conjectured that every pseudo algebraically closed field is C 1. We prove this conjecture in characteristic 0 by relating it to degenerations of Fano varieties.

AB - James Ax conjectured that every pseudo algebraically closed field is C 1. We prove this conjecture in characteristic 0 by relating it to degenerations of Fano varieties.

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U2 - 10.1007/s11856-007-0097-4

DO - 10.1007/s11856-007-0097-4

M3 - Article

AN - SCOPUS:58449100183

SN - 0021-2172

VL - 162

SP - 235

EP - 251

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

A conjecture of Ax and degenerations of Fano varieties

Abstract

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