The investigator proposes to explore in depth questions about the behaviour of the reductions modulo primes of abelian varieties and Drinfeld modules by means of analytic methods. Her motivation comes from conjectures formulated by S. Lang and H. Trotter (in the context of elliptic curves) in 1976, which, in turn, are related to classical open questions about prime numbers. The investigator's main research projects turn out to be related to a number of central problems in arithmetic geometry and analytic number theory. A coherent formulation of the main questions emerging from these projects, together with approaches and results towards their resolution, will contribute to the advancement of higher-dimensional analytic methods and their impact on arithmetic geometry.
This is research in the field of number theory. The central objects of study in number theory are, basically, prime numbers and Diophantine equations. The research done under this award concerns properties of prime numbers with additional interesting properties coming from geometric contexts. Apart from the intrinsic interest in these objects, their study has become even more appealing over the past years thanks to practical implications for cryptography and coding theory.
