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Polynomial bound for the nilpotency index of finitely generated nil algebras
作者：Mátyás Domokos
来源：[J].Algebra & Number Theory(IF 0.625), 2018, Vol.12 (5), pp.1233-1242MSP
摘要：Working over an infinite field of positivecharacteristic, an upperbound is given for the nilpotency indexof a finitely generated nilalgebra of bounded nil index $n$ in terms of the maximal degree ina minimal homogenous generating system of the ring of simultaneousconjugation inva...
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    Characterization of Kollár surfaces
    作者：Giancarlo Urzúa , José Yáñez
    来源：[J].Algebra & Number Theory(IF 0.625), 2018, Vol.12 (5), pp.1073-1105MSP
    摘要：Koll\'ar (2008) introduced the surfaces\[(x_1^{a_1}x_2+x_2^{a_2}x_3+x_3^{a_3}x_4+x_4^{a_4}x_1=0)\subset\P(w_1,w_2,w_3,w_4)\] where $w_i=W_i/w^*$,$W_i=a_{i+1}a_{i+2}a_{i+3}-a_{i+2}a_{i+3}+a_{i+3}-1$, and$w^*=\gcd(W_1,\dots,W_4)$. The aim was to give many interesting examplesof $\Q...
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      Local topological algebraicity with algebraic coefficients of analytic sets or functions
      作者：Guillaume Rond
      来源：[J].Algebra & Number Theory(IF 0.625), 2018, Vol.12 (5), pp.1215-1231MSP
      摘要：We prove that any complex or real analytic setor function germ is topologically equivalent to a germ defined bypolynomial equations whose coefficients are algebraic numbers.
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        Cohomology for Drinfeld doubles of some infinitesimal group schemes
        作者：Eric Friedlander , Cris Negron
        来源：[J].Algebra & Number Theory(IF 0.625), 2018, Vol.12 (5), pp.1281-1309MSP
        摘要：Consider a field $k$ of characteristic $p > 0$,the $r$-th Frobenius kernel $\mathbb{G}_{(r)}$ of a smooth algebraicgroup $\mathbb{G}$, theDrinfeld double $\operatorname{D}\mathbb{G}_{(r)}$ of $\mathbb{G}_{(r)}$, and a finitedimensional $\operatorname{D}\mathbb{G}_{(r)}$-module $M...
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          Correspondences without a core
          作者：Raju Krishnamoorthy
          来源：[J].Algebra & Number Theory(IF 0.625), 2018, Vol.12 (5), pp.1173-1214MSP
          摘要：We study the formal properties of correspondences of curves withouta core, focusing on the case of \'etale correspondences. The motivatingexamples come from Hecke correspondences of Shimura curves. Givena correspondence without a core, we construct an infinite graph$\mathcal{G}_{...
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            Certain abelian varieties bad at only one prime
            作者：Armand Brumer , Kenneth Kramer
            来源：[J].Algebra & Number Theory(IF 0.625), 2018, Vol.12 (5), pp.1027-1071MSP
            摘要：An abelian surface $A_{/\mathbb{Q}}$of prime conductor $N$ is {\em favorable}if its 2-division field $F$ is an $\mathcal S_5$-extension over$\mathbb{Q}$ withramification index 5 over $\mathbb{Q}_2$.Let $A$ be favorable and let $B$be a semistable abelian variety of dimension$2d$ a...
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              Représentations de réduction unipotente pourSO(2n + 1), III : Exemples de fronts d’onde
              作者：Jean-Loup Waldspurger
              来源：[J].Algebra & Number Theory(IF 0.625), 2018, Vol.12 (5), pp.1107-1171MSP
              摘要：\selectlanguage{french}Soit $G$ un groupe $\mathop{\operatorname{SO}}(2n+1)$ d\'efini sur uncorps $p$-adique. Nouscalculonsle front d'onde des repr\'esentations irr\'eductiblesanti-temp\'er\'ees de $G(F)$ qui sont de r\'eduction unipotente. Lefront d'onde d'unetelle repr\'esentat...
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                Arithmetic functions in short intervals and the symmetric group
                作者：Brad Rodgers
                来源：[J].Algebra & Number Theory(IF 0.625), 2018, Vol.12 (5), pp.1243-1279MSP
                摘要：\vspace*{-1pt}We consider the variance of sums of arithmetic functions over randomshort intervals in the function field setting. Based on the analogybetween factorizations of random elements of $\mathbb{F}_q[T]$ intoprimes and the factorizations of random permutations into cycles...
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                  Semistable Chow–Hall algebras of quivers andquantized Donaldson–Thomas invariants
                  作者：Hans Franzen , Markus Reineke
                  来源：[J].Algebra & Number Theory(IF 0.625), 2018, Vol.12 (5), pp.1001-1025MSP
                  摘要：The semistable ChowHa of a quiver with stability is defined as ananalog of the cohomological Hallalgebra of Kontsevich and Soibelmanvia convolution in equivariant Chow groups of semistable loci inrepresentation varieties of quivers. We prove several structuralresults on the semis...
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                    Positive scalar curvature and low-degree group homology
                    作者：Noé Bárcenas Torres , Rudolf Zeidler
                    来源：[J].Annals of K-Theory, 2018, Vol.3 (3), pp.565-579MSP
                    摘要：Let $\Gamma$ be a discrete group.Assuming rational injectivity of the Baum--Connes assembly map, weprovide new lower bounds on the rank of the positive scalar curvaturebordism group and the relative group in Stolz' positive scalar curvaturesequence for $\operatorname{B} \Gamma$.T...
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