Research
I work in the areas of Number Theory and Algebraic Geometry, because I study algebraic groups defined over number fields. The aim of my research is understanding how the properties of algebraic groups and their points can be detected from their reductions.
Publications
- On the order of the reductions of points on abelian varieties and tori, Ph.D. Thesis; pdf
- Prescribing valuations of the order of a point in the reductions of abelian varieties and tori, J. Number Theory, vol. 129 (2009), no.2, 469-476; arXiv.
- Two variants of the support problem for products of abelian varieties and tori, J. Number Theory, vol. 129 (2009), no.8, 1883-1892; arXiv.
- with Peter Jossen, A counterexample to the local-global principle of linear dependence for Abelian varieties , C. R. Acad. Sci. Paris, Ser. I 348 (2010), no.1, 9–10. Presented by J-P. Serre; arXiv.
- On the problem of detecting linear dependence for products of abelian varieties and tori, Acta Arith., vol. 142 (2010), no.2, 119-128; arXiv.
- L'ordine dei punti nelle riduzioni di varietà abeliane e tori, Unione Matematica Italiana, La Matematica nella società e nella cultura, Serie I, vol. 3 (2010), no.1, 128-131; pdf.
- On the reduction of points on abelian varieties and tori, Int. Math. Res. Notices, vol. 2011 (2011), no.7, 293-308; arXiv.
- The multilinear support problem for products of abelian varieties and tori, Int. J. Number Theory, vol. 8 (2012), no.1, 1-10; arXiv.
- with Chris Hall, On the prime divisors of the number of points on an elliptic curve, C. R. Acad. Sci. Paris, Ser. I 351 (2013) 1-3. Presented by J-P. Serre; arXiv.
- with Jeroen Demeyer, The constant of the support problem for abelian varieties, J. Number Theory, vol. 133 (2013), no.8, 2843-2856; arXiv.
- with Chris Hall, Characterizing abelian varieties by the reductions of the Mordell-Weil group, Pacific J. Math., vol. 265 (2013), no.2, 427-440; arXiv.
- The intersection of cyclic Kummer extensions with cyclotomic extensions; arXiv.
Links to coauthors: Jeroen Demeyer, Chris Hall, Peter Jossen