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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


IMPACT FACTOR 2018: 0.867

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Mathematical Citation Quotient (MCQ) 2017: 0.67

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Volume 30, Issue 6

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Group schemes and local densities of ramified hermitian lattices in residue characteristic 2. Part II

Sungmun Cho
  • Corresponding author
  • Graduate School of Mathematics, Kyoto University, Kitashirakawa, 606-8502, Kyoto, Japan; and POSTECH, Department of Mathematics, 7 Cheongam-ro, Nam-gu, Pohang-si, Gyeongsangbuk-do, 37673, Pohang, Republic of Korea
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Published Online: 2018-08-07 | DOI: https://doi.org/10.1515/forum-2017-0080

Abstract

This paper is the complementary work of [S. Cho, Group schemes and local densities of ramified hermitian lattices in residue characteristic 2: Part I, Algebra Number Theory 10 2016, 3, 451–532]. Ramified quadratic extensions E/F, where F is a finite unramified field extension of 2, fall into two cases that we call Case 1 and Case 2. In our previous work, we obtained the local density formula for a ramified hermitian lattice in Case 1. In this paper, we obtain the local density formula for the remaining Case 2, by constructing a smooth integral group scheme model for an appropriate unitary group. Consequently, this paper, combined with [W. T. Gan and J.-K. Yu, Group schemes and local densities, Duke Math. J. 105 2000, 3, 497–524] and our previous work, allows the computation of the mass formula for any hermitian lattice (L,H), when a base field is unramified over at a prime (2).

Keywords: local density; mass formula; group scheme; smooth integral model

MSC 2010: 11E41; 11E95; 14L15; 20G25; 11E39; 11E57

References

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    S. Cho, Group schemes and local densities of quadratic lattices in residue characteristic 2, Compos. Math. 151 (2015), no. 5, 793–827. CrossrefWeb of ScienceGoogle Scholar

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    S. Cho, Group schemes and local densities of ramified hermitian lattices in residue characteristic 2: Part I, Algebra Number Theory 10 (2016), no. 3, 451–532. Web of ScienceCrossrefGoogle Scholar

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    S. Cho, Group schemes and local densities of ramified hermitian lattices in residue characteristic 2: Part II, preprint (2018), https://arxiv.org/abs/1806.00726.

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    W. T. Gan and J.-K. Yu, Group schemes and local densities, Duke Math. J. 105 (2000), no. 3, 497–524. CrossrefGoogle Scholar

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About the article


Received: 2017-04-11

Published Online: 2018-08-07

Published in Print: 2018-11-01


Funding Source: Japan Society for the Promotion of Science

Award identifier / Grant number: KAKENHI Grant No. 16F16316

The author is partially supported by JSPS KAKENHI Grant No. 16F16316 and NRF 2018R1A4A 1023590.


Citation Information: Forum Mathematicum, Volume 30, Issue 6, Pages 1487–1520, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2017-0080.

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