Mod-2 Hecke algebras of level 3 and 5

• Shaunak V. Deo ^[2] ; Anna Medvedovsky ^[1]
  1. [1] University of Arizona

     University of Arizona

     Estados Unidos

     
  2. [2] Department of Mathematics, Indian Institute of Science, India
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 5, 2024
• Idioma: inglés
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• Resumen

  • We use deformation theory to study the big Hecke algebra acting on mod-2 modular forms of prime level N and all weights, especially its local component at the trivial representation. For N=3,5, we prove that the maximal reduced quotient of this big Hecke algebra is isomorphic to the maximal reduced quotient of the corresponding universal deformation ring. Then we completely determine the structure of this big Hecke algebra. We also describe a natural grading on mod-p Hecke algebras, and prove an R=T theorem for the partially full version of our mod-2 Hecke algebra.