On space filling curves and Albanese varieties

By Ofer Gabber. 2001

47 citations recorded by the source corpus.

Subfields: Computational Mechanics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/21b33f1175c1f49369fdca2550b9919e3ac34c79

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Bjorn Poonen

In Geometry and Topology

1. Dino J. Lorenzini
2. M. Raynaud
3. Qing Liu
4. Bjorn Poonen
5. Michael Stoll
6. Manjul Bhargava
7. Matthew Baker
8. D. Huybrechts

In Mathematical Physics

1. Bjorn Poonen
2. Dino J. Lorenzini
3. Qing Liu

Citations in the corpus

• Bertini theorems over finite fields (2002, background): “(2) It is also true that any abelian variety over a field k can be embedded as an abelian subvariety of the Jacobian of a smooth, projective, geometrically integral curve over k [ Gab01 ].”
• On the Brauer group of a surface (2005, background): “Proof of Theorem 1. Since a smooth proper surface over a field is projective (see, e.g., [7], 9.3.5), we may consider an embedding (over k )o fX into a projective space P n k . Gabber ([ 1 ], 1.6) proved that some hypersurface in P n k intersects X in a smooth section.”
• Integral p$p$-adic Hodge theory (2016, unknown): “Let X ⊂ D be a smooth and (sufficiently) ample hypersurface; this can be chosen over Z2: One has to arrange smoothness only over F2, so the result follows from the Bertini theorem over finite fields due to Gabber, [36], and more generally Poonen, [54].”