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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...
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...
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...
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...
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...
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...
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...
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.
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.
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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