motives, triangulated categories, weight structures, formal groups, group schemes
Main publications:
Mikhail V. Bondarko, “Weight structures vs. t-structures; weight filtrations, spectral sequences, and complexes (for motives and in general)”, Journal of K-Theory, 6:3 (2010), 387–504
Mikhail V. Bondarko, “Differential graded motives: weight complex, weight filtrations and spectral sequences for realizations; Voevodsky versus Hanamura”, Journal of the Institute of Mathematics of Jussieu, 8:1 (2009), 39–97
Mikhail V. Bondarko, “Motivically Functorial Coniveau Spectral Sequences; Direct Summands of Cohomology of Function Fields”, Documenta Mathematica, 2010, Suslin's volume, 33–117
M. V. Bondarko, K. S. Ladny, K. I. Pimenov, “Bases of associated Galois modules in general wildly ramified extensions and in elementary abelian extensions of degree $p^2$”, Chebyshevskii Sb., 26:4 (2025), 71–87
2024
2.
M. V. Bondarko, “Producing new semi-orthogonal decompositions in arithmetic geometry”, Mat. Sb., 215:4 (2024), 81–116; Sb. Math., 215:4 (2024), 511–542
Mikhail V. Bondarko, Sergei V. Vostokov, “Killing Weights from the Perspective of $t$-Structures”, Trudy Mat. Inst. Steklova, 320 (2023), 59–70; Proc. Steklov Inst. Math., 320 (2023), 51–61
2021
4.
M. V. Bondarko, D. Z. Kumallagov, “Smooth weight structures and birationality filtrations on motivic categories”, Algebra i Analiz, 33:5 (2021), 51–79; St. Petersburg Math. J., 33:5 (2022), 777–796
2020
5.
M. V. Bondarko, S. V. Vostokov, “The hearts of weight structures are the weakly idempotent complete categories”, Chebyshevskii Sb., 21:3 (2020), 29–38
6.
M. V. Bondarko, D. Z. Kumallagov, “On Chow-weight homology of motivic complexes and its relation to motivic homology”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7:4 (2020), 560–587; Vestn. St. Petersbg. Univ., Math., 7:4 (2020), 377–397
M. V. Bondarko, D. Z. Kumallagov, “On Chow weight structures without projectivity and resolution of singularities”, Algebra i Analiz, 30:5 (2018), 57–83; St. Petersburg Math. J., 30:5 (2019), 803–819
M. V. Bondarko, V. A. Sosnilo, “A nullstellensatz for triangulated categories”, Algebra i Analiz, 27:6 (2015), 41–56; St. Petersburg Math. J., 27:6 (2016), 889–898
M. V. Bondarko, M. A. Ivanov, “On Chow weight structures for $cdh$-motives with integral coefficients”, Algebra i Analiz, 27:6 (2015), 14–40; St. Petersburg Math. J., 27:6 (2016), 869–888
S. V. Vostokov, V. V. Volkov, M. V. Bondarko, “Explicit form of Hilbert symbol for polynomial formal groups over multidimensional local field. I”, Zap. Nauchn. Sem. POMI, 430 (2014), 53–60; J. Math. Sci. (N. Y.), 219:3 (2016), 370–374
M. V. Bondarko, A. V. Dievskii, “Non-abelian associated orders of wildly ramified local field extensions”, Zap. Nauchn. Sem. POMI, 356 (2008), 5–45; J. Math. Sci. (N. Y.), 156:6 (2009), 855–876
2007
12.
M. V. Bondarko, “Canonical Representatives in Strict Isomorphism Classes of Formal Groups”, Mat. Zametki, 82:2 (2007), 183–189; Math. Notes, 82:2 (2007), 159–164
M. V. Bondarko, “Leopoldt's problem for Abelian totally ramified extensions of complete discrete valuation fields”, Algebra i Analiz, 18:5 (2006), 99–129; St. Petersburg Math. J., 18:5 (2007), 757–778
M. V. Bondarko, “Classification of finite commutative group schemes over complete discrete valuation rings; the tangent space and semistable reduction of Abelian varieties”, Algebra i Analiz, 18:5 (2006), 72–98; St. Petersburg Math. J., 18:5 (2007), 737–755
M. V. Bondarko, “The generic fibre of finite group schemes; a “finite wild” criterion for good reduction of Abelian varieties”, Izv. RAN. Ser. Mat., 70:4 (2006), 21–52; Izv. Math., 70:4 (2006), 661–691
M. V. Bondarko, “Isogeny classes of formal groups over complete discrete valuation fields with an arbitrary residue field”, Algebra i Analiz, 17:6 (2005), 105–124; St. Petersburg Math. J., 17:6 (2006), 975–988
M. V. Bondarko, S. V. Vostokov, Kh. P. Minchev, “Restriction of the scalars for formal groups”, Zap. Nauchn. Sem. POMI, 319 (2004), 59–70; J. Math. Sci. (N. Y.), 134:6 (2006), 2477–2482
18.
M. V. Bondarko, S. V. Vostokov, F. Lorenz, “The Hilbert pairing for formal groups over $\sigma$-rings”, Zap. Nauchn. Sem. POMI, 319 (2004), 5–58; J. Math. Sci. (N. Y.), 134:6 (2006), 2445–2476
M. V. Bondarko, S. V. Vostokov, “An Explicit Classification of Formal Groups over Local Fields”, Trudy Mat. Inst. Steklova, 241 (2003), 43–67; Proc. Steklov Inst. Math., 241 (2003), 35–57
M. V. Bondarko, S. V. Vostokov, “Additive Galois modules in Dedekind rings. Decomposability”, Algebra i Analiz, 11:6 (1999), 103–121; St. Petersburg Math. J., 11:6 (2000), 1019–1033
M. V. Bondarko, S. V. Vostokov, “Decomposability of ideals as Galois modules in complete discrete valuation fields”, Algebra i Analiz, 11:2 (1999), 41–63; St. Petersburg Math. J., 11:1 (2000), 233–249
M. V. Bondarko, “Krull-Schmidt theorem for Henselian rings”, Zap. Nauchn. Sem. POMI, 265 (1999), 29–41; J. Math. Sci. (New York), 112:3 (2002), 4259–4265
23.
M. V. Bondarko, “Idempotents in the endomorphism ring of an ideal in a $p$-extension of a complete discrete valuation field with residue field of characteristic $p$ as a Galois module”, Zap. Nauchn. Sem. POMI, 265 (1999), 22–28; J. Math. Sci. (New York), 112:3 (2002), 4255–4258
B. Bekker, M. V. Bondarko, S. Vostokov, “Shafarevich bases in topological $K$-groups”, Algebra i Analiz, 10:2 (1998), 63–80; St. Petersburg Math. J., 10:2 (1999), 269–282
M. V. Bondarko, S. V. Vostokov, I. B. Zhukov, “Additive Galois modules in complete discrete valuation fields”, Algebra i Analiz, 9:4 (1997), 28–46; St. Petersburg Math. J., 9:4 (1998), 675–693
M. V. Bondarko, S. V. Vostokov, “A decomposition of ideals in an Abelian $p$-extension of complete discretely valuated fields.”, Zap. Nauchn. Sem. POMI, 236 (1997), 23–33; J. Math. Sci. (New York), 95:2 (1999), 2058–2064
M. V. Bondarko, I. B. Fesenko, “To the memory of Sergei Vladimirovich Vostokov”, Chebyshevskii Sb., 26:4 (2025), 33–36
28.
M. V. Bondarko, O. V. Demchenko, I. B. Zhukov, A. I. Madunts, P. N. Pital, Yu. V. Matiyasevich, V. N. Chubarikov, S. S. Demidov, V. M. Buchstaber, V. A. Bykovskii, M. A. Korolev, Yu. V. Nesterenko, U. M. Pachev, A. L. Semenov, V. G. Chirskii, N. M. Dobrovol'skii, N. N. Dobrovol'skii, I. Yu. Rebrova, “Sergey Vladimirovich Vostokov (13.04.1945 — 6.03.2025)”, Chebyshevskii Sb., 26:3 (2025), 416–418
2015
29.
D. G. Benua, M. V. Bondarko, N. A. Vavilov, M. A. Vsemirnov, A. I. Generalov, N. L. Gordeev, I. B. Zhukov, G. A. Leonov, B. B. Lur'e, I. A. Panin, A. L. Smirnov, I. B. Fesenko, A. V. Yakovlev, “To the anniversary of Sergei Vladimirovich Vostokov”, Algebra i Analiz, 27:6 (2015), 3–5; St. Petersburg Math. J., 27:6 (2016), 861–862
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