论文标题
关于弱的selmer群体的Leopoldt猜想和核心，在$ p $ adic-adic Lie Extensions中
On the weak Leopoldt conjecture and coranks of Selmer groups of supersingular abelian varieties in $p$-adic Lie extensions
论文作者
论文摘要
让$ a $是在数字字段$ f $上定义的Abelian品种，在所有$ f $ ther $ p $上的$ f $ suppellular降低。我们建立了弱点的猜想与经典Selmer $ a $ a $ a $ a $ a $ a $ a $ a $ a $的预期价值之间的等价性，而不是$ p $ ad的谎言扩展（不是neccesasasasiony含有cyclotomic $ \ zp $ - extension）。作为应用程序，我们获得了Selmer组定义顺序的确切性。如果$ p $ - 亚法谎言扩展是一维的，我们表明双selmer集团没有非平凡的有限subsodules。最后，我们表明，上述结论将其延续到了非凡的尖锐模块化形式的Selmer组。
Let $A$ be an abelian variety defined over a number field $F$ with supersingular reduction at all primes of $F$ above $p$. We establish an equivalence between the weak Leopoldt conjecture and the expected value of the corank of the classical Selmer group of $A$ over a $p$-adic Lie extension (not neccesasily containing the cyclotomic $\Zp$-extension). As an application, we obtain the exactness of the defining sequence of the Selmer group. In the event that the $p$-adic Lie extension is one-dimensional, we show that the dual Selmer group has no nontrivial finite submodules. Finally, we show that the aforementioned conclusions carry over to the Selmer group of a non-ordinary cuspidal modular form.
