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The modular approach to the Fermat equations of signature (p,p,p) and (p,p,2) over totally real fields

Time:Mon., 10:00-11:00 am, Oct. 28, 2024

Venue:C654, Shuangqing Complex Building

Organizer:Hansheng Diao, Heng Du, Yueke Hu, Bin Xu, Yihang Zhu

Speaker:Satyabrat Sahoo (YMSC)

BIMSA-YMSC Tsinghua Number Theory Seminar

Organizers:

Hansheng Diao, Heng Du, Yueke Hu, Bin Xu, Yihang Zhu

Speaker:

Satyabrat Sahoo (YMSC)

Time:

Mon., 10:00-11:00 am, Oct. 28, 2024

Venue:

C654, Shuangqing Complex Building

Title:

The modular approach to the Fermat equations of signature (p,p,p) and (p,p,2) over totally real fields

Abstract:

Let K be a totally real number field. In this talk, we will study the solutions of the Fermat equations of signature (p,p,p), (p,p,2) over K using the modular method. First, we study the asymptotic solutions of the equation x^p+y^p=2^rz^p with integers r>0 over K. Then, we study the asymptotic solutions of the equation x^p+y^p=z^2 over K. Finally, we provide several purely local criteria of K for these results.

DATEOctober 27, 2024
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