论文标题
在katz的$（a，b）$ - 指数款
On Katz's $(A,B)$-exponential sums
论文作者
论文摘要
我们使用$ \ ell $ -ADIC共同体和Denef-Loeser定理来推论Katz的定理（a，b）$ - 指数级的款项，以删除$ a+b $相对优质于特征性$ p $的假设。在某些退化的情况下，使用折叠分解和Adolphson-Sperber的$ L $ functions的程度改善了Betti数量估计值。在\ cite {w1}中应用面部分解定理，我们证明$（a，b）$ - polyenmials的通用家族在$ l $ function时通常是普通的，当$ l $ punctions $ p $处于某些算术中。
We deduce Katz's theorems for $(A,B)$-exponential sums over finite fields using $\ell$-adic cohomology and a theorem of Denef-Loeser, removing the hypothesis that $A+B$ is relatively prime to the characteristic $p$. In some degenerate cases, the Betti number estimate is improved using toric decomposition and Adolphson-Sperber's bound for the degree of $L$-functions. Applying the facial decomposition theorem in \cite{W1}, we prove that the universal family of $(A,B)$-polynomials is generically ordinary for its $L$-function when $p$ is in certain arithmetic progression.
