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pro vyhledávání: '"Achter, Jeff"'
After Jacobians of curves, Prym varieties are perhaps the next most studied abelian varieties. They turn out to be quite useful in a number of contexts. For technical reasons, there does not appear to be any systematic treatment of Prym varieties in
Externí odkaz:
http://arxiv.org/abs/2312.13263
We show that the image of a morphism of abelian schemes over a locally Noetherian base is again an abelian scheme.
Comment: 10 pages; comments welcome
Comment: 10 pages; comments welcome
Externí odkaz:
http://arxiv.org/abs/2312.13262
The classical Mordell-Weil theorem implies that an abelian variety $A$ over a number field $K$ has only finitely many $K$-rational torsion points. This finitude of torsion still holds even over the cyclotomic extension $K^{\rm cyc}=K\mathbb{Q}^{\math
Externí odkaz:
http://arxiv.org/abs/2305.19134
Albanese varieties provide a standard tool in algebraic geometry for converting questions about varieties in general, to questions about Abelian varieties. A result of Serre provides the existence of an Albanese variety for any geometrically connecte
Externí odkaz:
http://arxiv.org/abs/2210.05017
Publikováno v:
Mathematische Zeitschrift (2021)
For a complex projective manifold, Walker has defined a regular homomorphism lifting Griffiths' Abel-Jacobi map on algebraically trivial cycle classes to a complex abelian variety, which admits a finite homomorphism to the Griffiths intermediate Jaco
Externí odkaz:
http://arxiv.org/abs/2101.07506
We consider the connections among algebraic cycles, abelian varieties, and stable rationality of smooth projective varieties in positive characteristic. Recently Voisin constructed two new obstructions to stable rationality for rationally connected c
Externí odkaz:
http://arxiv.org/abs/2007.07470
For a smooth projective geometrically uniruled threefold defined over a perfect field we show that there exists a canonical abelian variety over the field, namely the second algebraic representative, whose rational Tate modules model canonically the
Externí odkaz:
http://arxiv.org/abs/2007.07180
Classically, regular homomorphisms have been defined as a replacement for Abel--Jacobi maps for smooth varieties over an algebraically closed field. In this work, we interpret regular homomorphisms as morphisms from the functor of families of algebra
Externí odkaz:
http://arxiv.org/abs/1911.09911
Publikováno v:
Alg. Number Th. 17 (2023) 1239-1280
Let $[X,\lambda]$ be a principally polarized abelian variety over a finite field with commutative endomorphism ring; further suppose that either $X$ is ordinary or the field is prime. Motivated by an equidistribution heuristic, we introduce a factor
Externí odkaz:
http://arxiv.org/abs/1905.11603
Autor:
Achter, Jeff
Publikováno v:
Algebraic Geometry 7 (2020), no. 5, 581--606
Several natural complex configuration spaces admit surprising uniformizations as arithmetic ball quotients, by identifying each parametrized object with the periods of some auxiliary object. In each case, the theory of canonical models of Shimura var
Externí odkaz:
http://arxiv.org/abs/1904.04288