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Fix an integer d > 0. In 2008, Chantal David and Tom Weston showed that, on average, an elliptic curve over Q picks up a nontrivial p-torsion point defined over a finite extension K of the p-adics of ...
GALOIS THEORY OF ITERATED MORPHISMS ON REDUCIBLE ELLIPTIC CURVES AND ABELIAN SURFACES WITH REAL MULTIPLICATION
Kummer map elliptic curves abelian surfaces with real multiplication
2014/12/8
Let $F$ be a number field and let $A$ be an abelian algebraic group defined over $F$. For a prime $\ell$ and a point $\alpha \in A(F)$, we obtain the tower of extensions $F([\ell^n]^{-1}(\alpha))$ by ...
Examples of abelian surfaces with non-square Tate-Shafarevich group
Examples of abelian surfaces non-square Tate-Shafarevich group Number Theory
2012/6/30
In this article we show the existence of abelian surfaces over Q with Tate-Shafarevich groups having orders five times a square and seven times a square. To obtain this result, we explore the invarian...
A Fourier-Mukai Approach to the Enumerative Geometry of Principally Polarized Abelian Surfaces
ideal sheaf Fourier-Mukai divisor abelian surface Hilbert scheme stable sheaf
2011/9/5
Abstract: We study twisted ideal sheaves of small length on an irreducible principally polarized abelian surface (T,l). Using Fourier-Mukai techniques we associate certain jumping schemes to such shea...
G-bundles on Abelian surfaces, hyperk\"aler manifolds, and stringy Hodge numbers
Abelian surfaces stringy Hodge numbers
2010/3/1
We study the moduli space MG (A) of flat G-bundles on an Abelian surface A, where G is a compact, simple, simply connected, connected Lie group. Equivalently, MG (A) is the (coarse) moduli space of s-...
Calabi-Yau Threefolds and Moduli of Abelian Surfaces I
Calabi-Yau Threefolds Moduli of Abelian Surfaces I
2010/10/29
We describe birational models and decide the rationality/unirationality of moduli spaces AA_{d} (and AA^{lev}_{d}) of (1,d)-polarized abelian surfaces (with canonical level structure, respectively) f...