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Irreducible characters with bounded root Artin conductor
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.
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    The structure of correlations of multiplicative functions at almost all scales, with applications to the Chowla and Elliott conjectures
    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...
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      Frobenius–Perron theory of endofunctors
      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.
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        Proof of a conjecture of Colliot-Thélène and adiophantine excision theorem
        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.
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          Brody hyperbolicity of base spaces of certain families of varieties
          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 ...
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            Positivity of anticanonical divisors and F-purityof fibers
            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...
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              A probabilistic approach to systems of parameters and Noether normalization
              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 ...
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                Degree of irrationality of very general abelian surfaces
                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 ...
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                  VI-modules in nondescribing characteristic, part I
                  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...
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                    Lower bounds for the least prime in Chebotarev
                    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...
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