Ph.D. student
Ph.D. student
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I am a Ph.D. student in mathematics at the Scuola Normale Superiore in Pisa.
I am a Ph.D. student in mathematics at the Scuola Normale Superiore in Pisa.
My research lies at the intersection of number theory and algebraic geoemtry.
My research lies at the intersection of number theory and algebraic geoemtry.
I explore how the geometry of algebraic varieties reflects in their Galois representations.
I explore how the geometry of algebraic varieties reflects in their Galois representations.
Contact me: andrea.gallese@sns.it
Research Interests
Research Interests
Some problems I have been thinking about.
The connected monodromy field. Let A be an abelian variety defined over a number field k, and consider its associated ℓ-adic Galois representation. The group of components of the image of representation naturally identifies with the Galois group of a finite extension k(eA)/k. This extension is independent of the prime ℓ and, remarkably, coincides with the field of definition of all Tate classes on powers of A. A natural question is: how can one compute this field explicitly?
Splitting Jacobians. 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?
Master thesis
Bachelor thesis
Curriculum VitaeCurriculum Vitae
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