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Izv. RAN. Ser. Mat., 1993, Volume 57, Issue 4, Pages 153–173 (Mi izv863)  

This article is cited in 9 scientific papers (total in 9 papers)

Algebraic cycles on a real algebraic GM-manifold and their applications

V. A. Krasnov


Abstract: For an algebraic cycle $Y\in A_k(X)$ on a real algebraic $\operatorname{GM}$-manifold $X$, the relationship between the homology classes $[Y(\mathbf C)]\in H_{2k}(X(\mathbf C),\mathbf Z)$ and $[Y(\mathbf R)]\in H_k(X(\mathbf R),\mathbf F_2)$ is studied. It is shown that similar relations hold for smooth cycles on a $\operatorname{GM}$-surface. The results are applied to prove congruences for the Euler characteristic of the set $X(\mathbf R)$.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1994, 43:1, 141–160

Bibliographic databases:

UDC: 513.6+517.6
MSC: 14C15, 14C30, 14F25, 14F45, 14J40, 32J25
Received: 20.05.1991

Citation: V. A. Krasnov, “Algebraic cycles on a real algebraic GM-manifold and their applications”, Izv. RAN. Ser. Mat., 57:4 (1993), 153–173; Russian Acad. Sci. Izv. Math., 43:1 (1994), 141–160

Citation in format AMSBIB
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\by V.~A.~Krasnov
\paper Algebraic cycles on a real algebraic GM-manifold and their applications
\jour Izv. RAN. Ser. Mat.
\yr 1993
\vol 57
\issue 4
\pages 153--173
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\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1994IzMat..43..141K}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1994
\vol 43
\issue 1
\pages 141--160
\crossref{https://doi.org/10.1070/IM1994v043n01ABEH001554}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Krasnov, “On cohomology classes defined by the real points of a real algebraic $\operatorname{GM}$-surface”, Russian Acad. Sci. Izv. Math., 43:2 (1994), 385–395  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. A. Krasnov, “On equivariant Grothendieck cohomology of a real algebraic variety, and its applications”, Russian Acad. Sci. Izv. Math., 44:3 (1995), 461–477  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. V. A. Krasnov, “The equivariant cohomology groups of a real algebraic surface and their applications”, Izv. Math., 60:6 (1996), 1193–1217  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. V. A. Krasnov, “Picard and Lefschetz numbers of real algebraic surfaces”, Math. Notes, 63:6 (1998), 747–751  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. V. A. Krasnov, “Real algebraic GM-varieties”, Izv. Math., 62:3 (1998), 465–491  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. V. A. Krasnov, “On the Fano Surface of a Real Cubic $M$-Threefold”, Math. Notes, 78:5 (2005), 662–668  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. V. A. Krasnov, “On Bordisms of Real Algebraic $M$-Varieties”, Math. Notes, 81:5 (2007), 649–655  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. V. A. Krasnov, “Real algebraic varieties and cobordism”, Izv. Math., 71:3 (2007), 573–601  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. S. R. Gallyamov, S. A. Melchukov, “Ideya Khodzha v perkolyatsii: otsenka poroga protekaniya po elementarnoi yacheike”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 4, 60–79  mathnet
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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