Differential descent obstructions over function fields
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- by José Felipe Voloch PDF
- Proc. Amer. Math. Soc. 142 (2014), 3421-3424 Request permission
Abstract:
We study a new obstruction to the existence of integral and rational points for algebraic varieties over function fields, the differential descent obstruction. We prove that this is the only obstruction to the existence of integral points in affine varieties in characteristic zero and also, in most cases, for rational points on curves in arbitrary characteristic.References
- A. Buium, Intersections in jet spaces and a conjecture of S. Lang, Ann. of Math. (2) 136 (1992), no. 3, 557–567. MR 1189865, DOI 10.2307/2946600
- Alexandru Buium, Geometry of differential polynomial functions. I. Algebraic groups, Amer. J. Math. 115 (1993), no. 6, 1385–1444. MR 1254738, DOI 10.2307/2374970
- Alexandru Buium, Geometry of differential polynomial functions. II. Algebraic curves, Amer. J. Math. 116 (1994), no. 4, 785–818. MR 1287940, DOI 10.2307/2375002
- Alexandru Buium and José Felipe Voloch, Lang’s conjecture in characteristic $p$: an explicit bound, Compositio Math. 103 (1996), no. 1, 1–6. MR 1404995
- E. R. Kolchin, Differential algebraic groups, Pure and Applied Mathematics, vol. 114, Academic Press, Inc., Orlando, FL, 1985. MR 776230
- David Harari and José Felipe Voloch, Descent obstructions and Brauer-Manin obstruction in positive characteristic, J. Inst. Math. Jussieu 12 (2013), no. 3, 545–551. MR 3062870, DOI 10.1017/S1474748012000758
- Bjorn Poonen and José Felipe Voloch, The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields, Ann. of Math. (2) 171 (2010), no. 1, 511–532. MR 2630046, DOI 10.4007/annals.2010.171.511
Additional Information
- José Felipe Voloch
- Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
- MR Author ID: 179265
- ORCID: 0000-0003-1669-9306
- Email: voloch@math.utexas.edu
- Received by editor(s): October 31, 2012
- Published electronically: June 26, 2014
- Communicated by: Matthew A. Papanikolas
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 3421-3424
- MSC (2010): Primary 11G35, 14G17
- DOI: https://doi.org/10.1090/S0002-9939-2014-12189-7
- MathSciNet review: 3238418