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Mat. Sb., 2015, Volume 206, Number 11, Pages 19–60 (Mi msb8523)  

This article is cited in 7 scientific papers (total in 7 papers)

Coefficient rings of formal group laws

V. M. Buchstaberab, A. V. Ustinovc

a Steklov Mathematical Institute of Russian Academy of Sciences
b Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
c Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences

Abstract: We describe the coefficient rings of universal formal group laws which arise in algebraic geometry, algebraic topology and their application to mathematical physics. We also describe the homomorphisms of these coefficient rings coming from reductions of one formal group law to another. The proofs are based on the number-theoretic properties of binomial coefficients.
Bibliography: 37 titles.

Keywords: formal group law, addition law, binomial coefficients, Hirzebruch genus.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00537-a
14-01-00203-а
This work was supported by the Russian Foundation for Basic Research (first author: grant no. 14-01-00537a; second author: grant no. 14-01-00203a).


DOI: https://doi.org/10.4213/sm8523

Full text: PDF file (791 kB)
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English version:
Sbornik: Mathematics, 2015, 206:11, 1524–1563

Bibliographic databases:

Document Type: Article
UDC: 512.741+517.583
MSC: 14L05, 55N22
Received: 26.03.2015 and 14.09.2015

Citation: V. M. Buchstaber, A. V. Ustinov, “Coefficient rings of formal group laws”, Mat. Sb., 206:11 (2015), 19–60; Sb. Math., 206:11 (2015), 1524–1563

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. Yu. Bunkova, V. M. Buchstaber, A. V. Ustinov, “Coefficient rings of Tate formal groups determining Krichever genera”, Proc. Steklov Inst. Math., 292 (2016), 37–62  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. E. Yu. Bunkova, “Elliptic function of level $4$”, Proc. Steklov Inst. Math., 294 (2016), 201–214  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. Z. Lü, T. Panov, “On toric generators in the unitary and special unitary bordism rings”, Algebr. Geom. Topol., 16:5 (2016), 2865–2893  crossref  mathscinet  zmath  isi  elib  scopus
    4. A. V. Ustinov, “Buchstaber Formal Group and Elliptic Functions of Small Levels”, Math. Notes, 102:1 (2017), 81–91  mathnet  crossref  crossref  mathscinet  isi  elib
    5. Elena Yu. Bunkova, “Hirzebruch functional equation: classification of solutions”, Proc. Steklov Inst. Math., 302 (2018), 33–47  mathnet  crossref  crossref  isi  elib
    6. A. V. Ustinov, “O formalnykh gruppakh Bukhshtabera spetsialnogo vida”, Matem. zametki, 105:6 (2019), 899–910  mathnet  crossref
    7. I. Yu. Limonchenko, T. E. Panov, G. S. Chernykh, “$SU$-bordizmy: strukturnye rezultaty i geometricheskie predstaviteli”, UMN, 74:3(447) (2019), 95–166  mathnet  crossref
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