منابع مشابه
Descent for Shimura Varieties
Wildeshaus and others have pointed out to me that it is not obvious that the descent maps on a Shimura variety given by Langlands’s Conjugacy Conjecture (Langlands 1979, Section 6) satisfy the continuity condition required for the descent to be effective. The following provides one proof of this (maybe not the best). Since the family (fσ) satisfying the conditions (a,b,c) below is unique (by th...
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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 that 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.
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It is well-known that the existence of non–algebraic Z/2–homology classes of a real algebraic manifold Y is equivalent to the existence of non–algebraic elements of the unoriented bordism group of Y and generates (first order) obstructions which prevent the possibility of realizing algebraic properties of smooth objects defined on Y . The main aim of this paper is to investigate the existence o...
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We study the section conjecture of anabelian geometry and the sufficiency of the finite descent obstruction to the Hasse principle for the moduli spaces of principally polarized abelian varieties and of curves over number fields. For the former we show that both the section conjecture and the finite descent obstruction fail in a very controlled way. For the latter, we prove some partial results...
متن کاملDescent obstructions and Brauer-Manin obstruction in positive characteristic
We prove that the Brauer-Manin obstruction is the only obstruction to the existence of integral points on affine varieties over global fields of positive characteristic p. More precisely, we show that the only obstructions come from étale covers of exponent p or, alternatively, from flat covers coming from torsors under connected group schemes of exponent p.
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2011
ISSN: 1944-7833,1937-0652
DOI: 10.2140/ant.2011.5.431