作者：Amalia Pizarro-Madariaga 来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (9), pp.1997-2004MSP 摘要：We prove that the best possible lower bound for theArtin conductor is exponential in the degree.
 作者：Terence Tao , Joni Teräväinen 来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (9), pp.2103-2150MSP 摘要：We study the asymptotic behaviour of higherorder correlations$\mathbb{E}_{n \leq X/d} g_1(n+ah_1) \cdots g_k(n+ah_k)$as a function of the parameters $a$ and $d$, where $g_1,\ldots,g_k$are bounded multiplicative functions, $h_1,\ldots,h_k$ are integershifts, and $X$ is large. Ou...
 作者：Jianmin Chen , Zhibin Gao , Elizabeth Wicks ... 来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (9), pp.2005-2055MSP 摘要：We introduce the Frobenius--Perron dimension of an endofunctor of a$\Bbbk$-linear category and provide someapplications.
 作者：Jan Denef 来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (9), pp.1983-1996MSP 摘要：We prove a conjecture of Colliot-Th\'{e}l\`{e}ne that impliesthe Ax--Kochen Theorem on $p$-adic forms. We obtain it as an easyconsequence of a diophantine excision theorem whose proof forms thebody of the present paper.
 作者：Mihnea Popa , Behrouz Taji , Lei Wu 来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (9), pp.2205-2242MSP 摘要：We prove that quasi-projective base spaces of smooth families ofminimal varieties of general typewith maximal variation do not admit Zariski dense entire curves. Wededuce the fact thatmoduli stacks of polarized varieties of this sort are Brody hyperbolic,answering a special case ...
 作者：Sho Ejiri 来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (9), pp.2057-2080MSP 摘要：We prove that given a flat generically smooth morphismbetween smooth projective varieties with $F$-pure closed fibers,if the source space is Fano, weak Fano or a variety with nefanticanonical divisor,respectively, then so is the target space.We also show that, in arbitrary charac...
 作者：Juliette Bruce , Daniel Erman 来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (9), pp.2081-2102MSP 摘要：We study systems of parameters over finite fields from a probabilisticperspective and use this to give the first effective Noethernormalization result over a finite field. Our central techniqueis an adaptation of Poonen's closed point sieve, where we sieveover higher dimensional ...
 作者：Nathan Chen 来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (9), pp.2191-2198MSP 摘要：The degree of irrationality of a projective variety $X$ is definedto be the smallest degree of a rationaldominant map to a projective spaceof the same dimension. For abelian surfaces, Yoshihara computed thisinvariant in specific cases, while Stapleton gave a sublinear upperbound ...
 作者：Rohit Nagpal 来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (9), pp.2151-2189MSP 摘要：Let VI be the category of finite dimensional$\mathbb{F}_q$-vector spaces whose morphisms are injective linear mapsand let $\mathbold{k}$ be a noetherian ring. We study the categoryof functors from VI to $\mathbold{k}$-modules in thecase when $q$ is invertible in $\mathbold{k}$. O...
 作者：Andrew Fiori 来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (9), pp.2199-2203MSP 摘要：In this paper we show there exists an infinite family of numberfields $L$, Galois over $\mathbb{Q}$, for which the smallest prime $p$of $\mathbb{Q}$ which splits completely in $L$has size at least $( \log(\lvert D_L\rvert ) )^{2+o(1)}$. Thisgives a converse to various upper bound...