论文标题
$ {\ rm gl} _2 $和$ p $ -adic $ l $ functions的伊瓦沙（Iwasawa）主要猜想
The Iwasawa Main Conjectures for ${\rm GL}_2$ and derivatives of $p$-adic $L$-functions
论文作者
论文摘要
我们证明了在不确定环境中以$ p $ p $的模块化形式的温和假设下的三变量伊瓦岛主要猜想。我们的结果是在Skinner-Urban的工作中进行了互补的设置，并且它适用于Greenberg对第一衍生物的非泛滥猜想，该衍生物是$ p $ p $ ad的$ -ADIC $ l $ L $ l $ l $ - 在HIDA家族中具有$ -1 $ $ -1且霍华德的公开非危险猜想的HIDA家庭中的cuSP形式。
We prove under mild hypotheses the three-variable Iwasawa main conjecture for $p$-ordinary modular forms in the indefinite setting. Our result is in a setting complementary to that in the work of Skinner-Urban, and it has applications to Greenberg's nonvanishing conjecture for the first derivatives at the center of $p$-adic $L$-functions of cusp forms in Hida families with root number $-1$ and to Howard's horizontal nonvanishing conjecture.
