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Uspekhi Mat. Nauk, 1969, Volume 24, Issue 5(149), Pages 3–86 (Mi umn5544)  

This article is cited in 30 scientific papers (total in 31 papers)

Lectures on the $K$-functor in algebraic geometry

Yu. I. Manin


Full text: PDF file (7894 kB)
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English version:
Russian Mathematical Surveys, 1969, 24:5, 1–89

Bibliographic databases:

UDC: 513.015.7
MSC: 16E30, 16W70, 16E20, 19L20, 19L10, 00B05
Received: 10.05.1969

Citation: Yu. I. Manin, “Lectures on the $K$-functor in algebraic geometry”, Uspekhi Mat. Nauk, 24:5(149) (1969), 3–86; Russian Math. Surveys, 24:5 (1969), 1–89

Citation in format AMSBIB
\Bibitem{Man69}
\by Yu.~I.~Manin
\paper Lectures on the $K$-functor in algebraic geometry
\jour Uspekhi Mat. Nauk
\yr 1969
\vol 24
\issue 5(149)
\pages 3--86
\mathnet{http://mi.mathnet.ru/umn5544}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=265355}
\zmath{https://zbmath.org/?q=an:0199.55502|0204.21302}
\transl
\jour Russian Math. Surveys
\yr 1969
\vol 24
\issue 5
\pages 1--89
\crossref{https://doi.org/10.1070/RM1969v024n05ABEH001357}


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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. I. V. Dolgachev, “The Euler characteristic of a family of algebraic varieties”, Math. USSR-Sb., 18:2 (1972), 303–319  mathnet  crossref  mathscinet  zmath
    2. Dan Laksov, “Algebraic cycles on Grassmann varieties”, Advances in Mathematics, 9:3 (1972), 267  crossref
    3. L. N. Vaserstein, “Foundations of algebraic $K$-theory”, Russian Math. Surveys, 31:4 (1976), 89–156  mathnet  crossref  mathscinet  zmath
    4. E.Graham Evans, “Bourbaki's theorem and algebraic K-theory”, Journal of Algebra, 41:1 (1976), 108  crossref
    5. V. A. Iskovskikh, “Fano 3-folds. I”, Math. USSR-Izv., 11:3 (1977), 485–527  mathnet  crossref  mathscinet  zmath
    6. V. I. Danilov, “The geometry of toric varieties”, Russian Math. Surveys, 33:2 (1978), 97–154  mathnet  crossref  mathscinet  zmath
    7. Gert Almkvist, “K-theory of endomorphisms”, Journal of Algebra, 55:2 (1978), 308  crossref
    8. Ch. Kratzer, “λ-Structure enK-théorie algébrique”, Comment Math Helv, 55:1 (1980), 233  crossref  mathscinet  zmath  isi
    9. V. I. Danilov, “Decomposition of certain birational morphisms”, Math. USSR-Izv., 16:2 (1981), 419–429  mathnet  crossref  mathscinet  zmath  isi
    10. I. V. Demin, “Fano threefolds representable in the form of line bundles”, Math. USSR-Izv., 17:1 (1981), 219–226  mathnet  crossref  mathscinet  zmath  isi
    11. Howard L. Hiller, “λ-rings and algebraic K-theory”, Journal of Pure and Applied Algebra, 20:3 (1981), 241  crossref
    12. V. G. Sarkisov, “On conic bundle structures”, Math. USSR-Izv., 20:2 (1983), 355–390  mathnet  crossref  mathscinet  zmath
    13. V. S. Kulikov, “Calculation of singularities of an imbedding of a generic algebraic surface in projective space $\mathbb{P}^3$”, Funct. Anal. Appl., 17:3 (1983), 176–186  mathnet  crossref  mathscinet  zmath  isi
    14. Dirk-Jan Smit, “String theory and algebraic geometry of moduli spaces”, Comm Math Phys, 114:4 (1988), 645  crossref  mathscinet  zmath  adsnasa  isi
    15. A. V. Pukhlikov, “Birational automorphisms of a three-dimensional quartic with a quadratic singularity”, Math. USSR-Sb., 63:2 (1989), 457–482  mathnet  crossref  mathscinet  zmath
    16. A. V. Pukhlikov, “Birational automorphisms of a double space and double quadric”, Math. USSR-Izv., 32:1 (1989), 233–243  mathnet  crossref  mathscinet  zmath
    17. A. N. Tyurin, “Symplectic structures on the varieties of moduli of vector bundles on algebraic surfaces with $p_g>0$”, Math. USSR-Izv., 33:1 (1989), 139–177  mathnet  crossref  mathscinet  zmath
    18. A. Al Amrani, “Groupe de Chow et K-théorie cohérente des espaces projectifs tordus”, K-Theory, 2:5 (1989), 579  crossref  mathscinet  zmath
    19. V. G. Drinfeld, V. A. Iskovskikh, A. I. Kostrikin, A. N. Tyurin, I. R. Shafarevich, “Yurii Ivanovich Manin (on his 60th birthday)”, Russian Math. Surveys, 52:4 (1997), 863–873  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    20. A. S. Tikhomirov, “The variety of complete pairs of zero-dimensional subschemes of an algebraic surface”, Izv. Math., 61:6 (1997), 1265–1291  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    21. Nikita A. Karpenko, “Three theorems on common splitting fields of central simple algebras”, Isr J Math, 111:1 (1999), 125  crossref  mathscinet  zmath  isi  elib
    22. Eric Sharpe, “D-branes, derived categories, and Grothendieck groups”, Nuclear Physics B, 561:3 (1999), 433  crossref
    23. E. N. Materov, “The Bott formula for toric varieties”, Mosc. Math. J., 2:1 (2002), 161–182  mathnet  crossref  mathscinet  zmath  elib
    24. Izuru Mori, S. Paul. Smith, “The Grothendieck group of a quantum projective space bundle”, K-Theory, 37:3 (2006), 263  crossref  mathscinet  zmath  isi
    25. Bohning, C, “Derived categories of coherent sheaves on rational homogeneous manifolds”, Documenta Mathematica, 11 (2006), 261  mathscinet  isi  elib
    26. S. G. Tankeev, “Monoidal transformations and conjectures on algebraic cycles”, Izv. Math., 71:3 (2007), 629–655  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    27. S. G. Tankeev, “On algebraic cycles on complex Abelian schemes over smooth projective curves”, Izv. Math., 72:4 (2008), 817–844  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    28. S. G. Tankeev, “On the standard conjecture for complex 4-dimensional elliptic varieties and compactifications of Néron minimal models”, Izv. Math., 78:1 (2014), 169–200  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    29. Sven Meinhardt, Holger Partsch, “Quotient categories, stability conditions, and birational geometry”, Geom Dedicata, 2014  crossref
    30. Ulrike Rieß, “On the Chow ring of birational irreducible symplectic varieties”, manuscripta math, 2014  crossref
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