The modular approach for solving $x^r+y^r=z^p$ over totally real number fields

Diana Mocanu
University of Warwick

Date(s) : 24/11/2022   iCal
12 h 00 min - 13 h 00 min

will first introduce the modular method for solving Diophantine Equations, famously used to prove the Fermat Last Theorem. Then, we will see how to generalize it for a totally real number field $K$ and a Fermat-type equation $Aa^p+Bb^q=Cc^r$ over $K$. We call the triple of exponents $(p,q,r)$ the signature of the equation. We will see various results concerning the solutions to the Fermat equation with signatures $(r,r,p)$ (fixed r). This will involve image of inertia comparison and the study of certain $S$-unit equations over $K$.
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