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Relevant bibliographies by topics / Maximal unramified extensions

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Academic literature on the topic 'Maximal unramified extensions'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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Journal articles on the topic "Maximal unramified extensions"

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Boston, Nigel, and Melanie Matchett Wood. "Non-abelian Cohen–Lenstra heuristics over function fields." Compositio Mathematica 153, no. 7 (2017): 1372–90. http://dx.doi.org/10.1112/s0010437x17007102.

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Boston, Bush and Hajir have developed heuristics, extending the Cohen–Lenstra heuristics, that conjecture the distribution of the Galois groups of the maximal unramified pro-$p$extensions of imaginary quadratic number fields for$p$an odd prime. In this paper, we find the moments of their proposed distribution, and further prove there is a unique distribution with those moments. Further, we show that in the function field analog, for imaginary quadratic extensions of$\mathbb{F}_{q}(t)$, the Galois groups of the maximal unramified pro-$p$extensions, as$q\rightarrow \infty$, have the moments pred

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ITOH, TSUYOSHI, and YASUSHI MIZUSAWA. "On tamely ramified pro-p-extensions over -extensions of." Mathematical Proceedings of the Cambridge Philosophical Society 156, no. 2 (2013): 281–94. http://dx.doi.org/10.1017/s0305004113000637.

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AbstractFor an odd prime number p and a finite set S of prime numbers congruent to 1 modulo p, we consider the Galois group of the maximal pro-p-extension unramified outside S over the ${\mathbb Z}_p$-extension of the rational number field. In this paper, we classify all S such that the Galois group is a metacyclic pro-p group.

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Ozaki, Manabu. "Construction of maximal unramified p-extensions with prescribed Galois groups." Inventiones mathematicae 183, no. 3 (2010): 649–80. http://dx.doi.org/10.1007/s00222-010-0289-0.

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SASAKI, SOSUKE. "DISTRIBUTION OF GALOIS GROUPS OF MAXIMAL UNRAMIFIED 2-EXTENSIONS OVER IMAGINARY QUADRATIC FIELDS." Nagoya Mathematical Journal 237 (July 9, 2018): 166–87. http://dx.doi.org/10.1017/nmj.2018.16.

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Let $k$ be an imaginary quadratic field with $\operatorname{Cl}_{2}(k)\simeq V_{4}$. It is known that the length of the Hilbert $2$-class field tower is at least $2$. Gerth (On 2-class field towers for quadratic number fields with$2$-class group of type$(2,2)$, Glasgow Math. J. 40(1) (1998), 63–69) calculated the density of $k$ where the length of the tower is $1$; that is, the maximal unramified $2$-extension is a $V_{4}$-extension. In this paper, we shall extend this result for generalized quaternion, dihedral, and semidihedral extensions of small degrees.

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Odai, Yoshitaka. "On unramified cyclic extensions of degree l of algebraic number fields of degree l." Nagoya Mathematical Journal 107 (September 1987): 135–46. http://dx.doi.org/10.1017/s0027763000002580.

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Let I be an odd prime number and let K be an algebraic number field of degree I. Let M denote the genus field of K, i.e., the maximal extension of K which is a composite of an absolute abelian number field with K and is unramified at all the finite primes of K. In [4] Ishida has explicitly constructed M. Therefore it is of some interest to investigate unramified cyclic extensions of K of degree l, which are not contained in M. In the preceding paper [6] we have obtained some results about this problem in the case that K is a pure cubic field. The purpose of this paper is to extend those result

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Yamamura, Ken. "Maximal unramified extensions of imaginary quadratic number fields of small conductors." Journal de Théorie des Nombres de Bordeaux 9, no. 2 (1997): 405–48. http://dx.doi.org/10.5802/jtnb.211.

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Yamamura, Ken. "Maximal unramified extensions of imaginary quadratic number fields of small conductors." Proceedings of the Japan Academy, Series A, Mathematical Sciences 73, no. 4 (1997): 67–71. http://dx.doi.org/10.3792/pjaa.73.67.

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Bartholdi, Laurent, and Michael R. Bush. "Maximal unramified 3-extensions of imaginary quadratic fields and SL2(Z3)." Journal of Number Theory 124, no. 1 (2007): 159–66. http://dx.doi.org/10.1016/j.jnt.2006.08.008.

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Mizusawa, Yasushi. "On the maximal unramified pro-2-extension of Z2-extensions of certain real quadratic fields." Journal of Number Theory 105, no. 2 (2004): 203–11. http://dx.doi.org/10.1016/j.jnt.2003.10.002.

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Yamamura, Ken. "Maximal unramified extensions of imaginary quadratic number fields of small conductors, II." Journal de Théorie des Nombres de Bordeaux 13, no. 2 (2001): 633–49. http://dx.doi.org/10.5802/jtnb.341.

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Dissertations / Theses on the topic "Maximal unramified extensions"

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Wong, Ka Lun. "Maximal Unramified Extensions of Cyclic Cubic Fields." BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/2781.

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Maximal unramified extensions of quadratic number fields have been well studied. This thesis focuses on maximal unramified extensions of cyclic cubic fields. We use the unconditional discriminant bounds of Moreno to determine cyclic cubic fields having no non-solvable unramified extensions. We also use a theorem of Roquette, developed from the method of Golod-Shafarevich, and some results by Cohen to construct cyclic cubic fields in which the unramified extension is of infinite degree.

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Book chapters on the topic "Maximal unramified extensions"

1

Scholze, Peter, and Jared Weinstein. "v-sheaves associated with perfect and formal schemes." In Berkeley Lectures on p-adic Geometry. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691202082.003.0018.

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This chapter explores v-sheaves associated with perfect and formal schemes. The more general formalism of v-sheaves makes it possible to consider not only analytic adic spaces as diamonds, but also certain non-analytic objects as v-sheaves. The chapter first analyzes the behavior on topological spaces. Let X be any pre-adic space over Zp. This is not a diamond, but the chapter shows that it is a v-sheaf. It assesses some properties of this construction. The chapter then looks at applications to local models and integral models of Rapoport-Zink spaces. By passage to the maximal unramified extension and Galois descent, one can assume that k is algebraically closed.

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