Ph.D. student

Contact me: andrea.gallese@sns.it

Research Interests

Some problems I have been thinking about:

• The field over which the monodromy group gets connected. Let A be an abelian variety defined over a number field K. Consider the corresponding Galois representation on the absolute Galois group G of K on the Tate module of the abelian variety. The monodromy group G_l of the representation is by definition the Zariski closure of the image of said representation, it is an algebraic group over Q_l. This group might not be connected. In that case, G_l/G_l^0 is finite, and over a finite field extension L/K it becomes connected. This field extension is independent of the prime l. How can we compute this field explicitly? 

• Splitting of the Jacobian of a genus 2 cover of an elliptic curve. Let f: Y -> X be a ramified cover from a complex curve of genus 2 to a complex curve of genus 1. The Jacobian of Y is isogenous to the product of two elliptic curves, one of which is X. How can we determine the other one?