On the reduction modulo p of certain modular p-adic Galois representations

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• 作者：Abhik Ganguli ^{aganguli@iisermohali.ac.in" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Galois representations ; Modular forms ; Hilbert modular forms ; Modular Galois representations ; Mod p reduction of Galois representations
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：172
• 期：Complete
• 页码：392-412
• 全文大小：511 K

文摘

We determine the possible Serre weights associated to certain Hilbert modular forms when the rational prime p is totally ramified in the totally real field F. Our weight lowering method for arbitrarily large weight is applicable when the slope is sufficiently small, enabling us to compute the mod p reduction at inertia from the known results in the small weight range. In the case of elliptic modular forms (and for certain Hilbert modular forms in the p totally split case) we obtain a unique mod p   reduction when the slope is in (0,1/2)$(0,1/2)$.