Potential automorphy and change of weight
Potential automorphy and change of weight
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潜在的自同构和重量变化
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Richard Taylor
中科院分区：
文献类型：
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作者：
Thomas Barnet;Toby Gee;D. Geraghty;Richard Taylor
我们证明了一个自同构提升定理的L-进表示，我们施加了一个新的条件在l，我们称之为潜在的对角化。“这个结果允许改变重量”，似乎是实质上更灵活的比以前的定理沿着相同的路线。我们得到几个应用程序。例如，我们证明了全真实的域的绝对Galois群的任何不可约的、全奇的、本质自对偶的、正则的、弱相容的l-adic表示系统都是潜在自同构的，因此是纯的，并且它的L-函数对整个复平面具有亚纯延拓，满足期望的函数方程.
We prove an automorphy lifting theorem for l-adic representations where we impose a new condition at l, which we call potentential diagonalizability." This result allows for change of weight" and seems to be substantially more exible than previous theorems along the same lines. We derive several applications. For instance we show that any irreducible, totally odd, essentially self-dual, regular, weakly compatible system of l-adic representations of the absolute Galois group of a totally real eld is potentially automorphic and hence is pure and its L-function has meromorphic continuation to the whole complex plane and satises the expected functional equation.