Robin de Jong
Robin de Jong
We show that there exists a sequence of genus three curves defined over the rationals in which the height of a canonical Gross-Schoen cycle tends to infinity. ...
George C Ţurcaş
George C Ţurcaş
Assuming a deep but standard conjecture in the Langlands programme, we prove Fermat's Last Theorem over Q ( i ) . Under the same assumption, we also prove that, for all prime exponents p ≥ 5 , Fermat's equation a p + b p + c p = 0 ...
Beth Romano,Jack A Thorne
Beth Romano
An ADE Dynkin diagram gives rise to a family of algebraic curves. In this paper, we use arithmetic invariant theory to study the integral points of the curves associated to the exceptional diagrams E 6 , E 7 , E 8 . These curves are non...
Clemens Fuchs,Christoph Hutle,Florian Luca
Clemens Fuchs
The study of Diophantine triples taking values in linear recurrence sequences is a variant of a problem going back to Diophantus of Alexandria which has been studied quite a lot in the past. The main questions are, as usual, about existence...