Explicit Serre weights for two-dimensional Galois representations over a ramified base

作者：M. Steinmetz · 发表于：Transactions of the American Mathematical Society · 年份：2022 · DOI：10.1090/tran/8794 · 被引用次数：2

<p>Given a totally real number field <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F"> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding="application/x-tex">F</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and a mod <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> Galois representation <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="rho colon upper G Subscript upper F Baseline right-arrow normal upper G normal upper L Subscript 2 Baseline left-parenthesis bold upper F overbar Subscript p Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>ρ</mml:mi> <mml:mo>:</mml:mo> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>F</mml:mi> </mml:msub> <mml:mo stretchy="false">→</mml:mo> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">G</mml:mi> <mml:mi mathvariant="normal">L</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mm...