This book presents several basic techniques in algebraic geometry, group representations,
number theory, l-adic and standard cohomology, and modular forms. It explores how NX (p) …

We show that abelian surfaces (and consequently curves of genus 2) over totally real fields
are potentially modular. As a consequence, we obtain the expected meromorphic …

A database of genus-2 curves over the rational numbers Page 1 LMS J. Comput. Math. 19 (Special
issue A) (2016) 235–254 C 2016 Authors doi:10.1112/S146115701600019X A database of …

We apply some of the latest techniques from machine-learning to the arithmetic of
hyperelliptic curves. More precisely we show that, with impressive accuracy and confidence …

Let g≥ 1, and let Q∈ Z [x] be a monic, squarefree polynomial of degree 2g+ 1. For an odd
prime p not dividing the discriminant of Q, let Zp (T) denote the zeta function of the …

Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time Page 1
LMS J. Comput. Math. 17 (Special issue A) (2014) 257–273 C 2014 Authors doi:10.1112/S1461157014000187 …

We study the geometry and arithmetic of the curves $ C\colon y^ 3= x^ 4+ ax^ 2+ b $ and
their associated Prym abelian surfaces $ P $. We prove a Torelli theorem in this context and …

Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time II Page
136 Contemporary Mathematics Volume 663 , 2016 http://dx. doi. org/10.1090/conm/663/13352 …

We announce the classification of Sato-Tate groups of abelian threefolds over number fields;
there are 410 possible conjugacy classes of closed subgroups of USp (6) that occur. We …

In this expository article we explore the relationship between Galois representations, motivic
L-functions, Mumford-Tate groups, and Sato-Tate groups, and we give an explicit …