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Examples of hypergeometric twistor𝒟-modules
作者：Alberto Castaño Domínguez , Thomas Reichelt , Christian Sevenheck
来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (6), pp.1415-1442MSP
摘要：We show that certain one-dimensional hypergeometric differentialsystemsunderlie objects of the category of irregular mixed Hodge modules,which was recentlyintroduced by Sabbah, and compute the irregular Hodge filtrationfor them. We also provide a comparison theorem between two di...
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    The congruence topology, Grothendieck duality and thin groups
    作者：Alexander Lubotzky , Tyakal Nanjundiah Venkataramana
    来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (6), pp.1281-1298MSP
    摘要：This paper answers a question raised by Grothendieck in 1970 on the``Grothendieck closure'' of an integral linear group and proves aconjecture of the first author made in 1980. This is done by a detailedstudy of the congruence topology of arithmetic groups, obtaining alongthe way...
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      An improved bound for the lengths of matrix algebras
      作者：Yaroslav Shitov
      来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (6), pp.1501-1507MSP
      摘要：Let $S$ be a set of $n\times n$ matrices over a field $\mathbb{F}$.We show that the $\mathbb{F}$-linear span of the words in $S$ of length at most\[2n\log_2n+4n\]is the full $\mathbb{F}$-algebra generated by $S$.This improves on the $\tfrac{n^2}3+\tfrac23$ bound by Paz (1984) and...
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        Positivity functions for curves on algebraic varieties
        作者：Brian Lehmann , Jian Xiao
        来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (6), pp.1243-1279MSP
        摘要：This is the second part of our work on Zariski decompositionstructures, where we compare two different volume type functions forcurve classes. The first function is the polar transform of the volumefor divisor classes. The second function captures the asymptoticgeometry of curves...
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          Unlikely intersections in semiabelian surfaces
          作者：Daniel Bertrand , Harry Schmidt
          来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (6), pp.1455-1473MSP
          摘要：We consider a family, depending on a parameter,of multiplicative extensions of an elliptic curve with complexmultiplications. They form a 3-dimensional variety $G$ which admitsa dense set of special curves, known as Ribet curves, which strictlycontains the torsion curves. We show...
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            Weyl bound for p-power twist of GL(2)L-functions
            作者：Ritabrata Munshi , Saurabh Kumar Singh
            来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (6), pp.1395-1413MSP
            摘要：Let $f$ be a cuspidal eigenform (holomorphic or Maass) for thecongruence group $\Gamma_0(N)$ with $N$ square-free. Let $p$ be aprime and let $\chi$ be a primitive character of modulus $p^{3r}$. Weshall prove the Weyl-type subconvex bound\[L\bigl(\tfrac{1}{2}+it,f\otimes \chi\bigr...
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              Congruences of parahoric group schemes
              作者：Radhika Ganapathy
              来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (6), pp.1475-1499MSP
              摘要：Let $F$ be a nonarchimedean local fieldand let $T$ be a torus over $F$. With $\mathcal{T}^{N\!R}$ denoting theN\'eron--Raynaud model of $T$, a result of Chai and Yu asserts thatthe model $\mathcal{T}^{N\!R} \times_{\mathfrak{O}_F}\mathfrak{O}_F/\mathfrak{p}_F^m$ is canonicallydet...
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                On the ramified class field theory of relative curves
                作者：Quentin Guignard
                来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (6), pp.1299-1326MSP
                摘要：We generalize Deligne's approach to tame geometricclass field theory to the case of a relative curve, with arbitraryramification.
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                  Blow-ups and class field theory for curves
                  作者：Daichi Takeuchi
                  来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (6), pp.1327-1351MSP
                  摘要：We propose another proof of geometric class field theory forcurves by considering blow-upsof symmetric products of curves.
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                    Algebraic monodromy groups of l-adicrepresentations of Gal(ℚ∕ℚ)
                    作者：Shiang Tang
                    来源：[J].Algebra & Number Theory(IF 0.625), 2019, Vol.13 (6), pp.1353-1394MSP
                    摘要：In this paper we prove that for any connected reductive algebraic group$G$ and a large enough prime $l$, there are continuous homomorphisms\[\operatorname{Gal}(\bar{\mathbb{Q}}/\mathbb{Q}) \toG(\bar{\mathbb{Q}}_l)\]with Zariski-dense image, in particular we produce the first such...
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