ÿþ<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN"> <HTML> <HEAD> <TITLE>Mikhail Borovoi's Publications</TITLE> <META NAME="GENERATOR" CONTENT="Mozilla/3.01Gold (X11; I; SunOS 4.1.3_U1 sun4c) [Netscape]"> </HEAD> <BODY TEXT="#333333" BGCOLOR="#FFFFFF"> <CENTER><H2>Publications<BR>Mikhail Borovoi </H2></CENTER> <OL> <li> M. Borovoi, C.D. Gonz&aacute;lez-Avil&eacute;s, <em>The algebraic fundamental group of a reductive group scheme over an arbitrary base scheme,</em> To appear in Cent. Eur. J. Math. <a href="http://arxiv.org/abs/1303.6586">arXiv:1303.6586 [math.AG]</a>. <p> <li> M. Borovoi, <em>On the unramified Brauer group of a homogeneous space,</em> to appear in Algebra i Analiz, <a href="http://arxiv.org/abs/1206.1023">arXiv:1206.1023 [math.AG]</a>. <p> <li> M. Borovoi, <a href="http://www.math.jussieu.fr/~demarche">C. Demarche</a> et <a href="http://www.math.u-psud.fr/~harari">D. Harari,</a> <em>Complexes de groupes de type multiplicatif et groupe de Brauer non ramifi&eacute des espaces homog&egrave;nes,</em> &Agrave para&icirc;tre aux Ann. Sci. &Eacute;c. Norm. Sup&eacute;r., <a href="http://arxiv.org/abs/1203.5964">arXiv:1203.5964[math.AG]</a>. <p> <li> M. Borovoi, <a href="http://www.cs.biu.ac.il/~kunyav"> B. Kunyavskii</a>, <a href="http://www.math.uwo.ca/~nlemire/">N. Lemire</a>, and <a href="http://www.math.ubc.ca/~reichst">Z. Reichstein</a>, <em> Stably Cayley groups in characteristic zero,</em> Int. Math. Res. Notices 2013; doi: 10.1093/imrn/rnt123. <a href="http://arxiv.org/abs/1207.1329 ">arXiv:1207.1329 [math.AG]</a>, <a href="http://imrn.oxfordjournals.org/content/early/2013/06/28/imrn.rnt123.abstract?sid=f13d85fd-e43f-4770-a77b-3ae282d9ab55"> online</a>. <p> <li> M. Borovoi and <a href="http://www.math.jussieu.fr/~demarche">C. Demarche,</a> <em> Manin obstruction to strong approximation for homogeneous spaces,</em> Comment. Math. Helv. <b> 88 </b> (2013), 1-54. <a href="http://arxiv.org/abs/0912.0408"> arXiv:0912.0408[math.NT]</a>, <a href="http://www.ems-ph.org/journals/show_abstract.php?issn=0010-2571&vol=88&iss=1&rank=1">online</a>. <p> <li> M. Borovoi and T.M. Schlank, <em>A cohomological obstruction to weak approximation for homogeneous spaces,</em> Moscow Math. J. <b>12</b> (2012), 1-20, <a href="http://arxiv.org/abs/1012.1453">arXiv:1012.1453[math.NT]</a>, <a href="http://www.ams.org/journals/distribution/mmj/vol12-1-2012/borovoi-schlank.pdf">online</a>. <p> <li> M. Borovoi and J. van Hamel, <em>Extended equivariant Picard complexes and homogeneous spaces,</em> Transform. Groups <b>17</b> (2012), 51-86, <a href="http://arxiv.org/abs/1010.3414">arXiv:1010.3414[math.AG]</a>, <a href="http://www.springerlink.com/content/u53704364j362827/">online</a>. <p> <li> M. Borovoi, <em>Vanishing of algebraic Brauer-Manin obstructions,</em> J. Ramanujan Math. Soc. <b>26</b> (2011), 333-349, <a href="http://arxiv.org/abs/1012.1189">arXiv:1012.1189[math.NT]</a>. <p> <li> M. Borovoi, <em> Symmetric homogeneous spaces with finitely many orbits,</em> Appendix to the paper of A. Gorodnik and Hee Oh: <em>Rational points on homogeneous varieties and equidistribution of adelic periods, </em> Geom. Funct. Anal., <b>21</b> (2011), 319--392, <a href="http://arxiv.org/abs/0803.1996">arXiv:0803.1996[math.AG]</a>, <a href="http://www.springerlink.com/content/blt241t75v017w4p/">online</a>. <p> <li> M. Borovoi and <a href="http://www.math.ubc.ca/~reichst">Z. Reichstein</a>, <em> Toric-friendly groups,</em> Algebra Number Theory <b>5</b> (2011), 361-378, <a href="http://arxiv.org/abs/1003.5894"> arXiv:1003.5894[math.AG]</a>, <a href="http://msp.berkeley.edu/ant/2011/5-3/p03.xhtml">online</a>. <p> <li> M. Borovoi, <em> The defect of weak approximation for homogeneous spaces, II, </em> Dal'nevost. Mat. Zh. <b>9</b> (2009), 15-23, <a href="http://arxiv.org/abs/0804.4767"> arXiv:0804.4767 [math.NT]</a>, <a href="http://www.mathnet.ru/links/5f24437fe5a9b87330634f9c60bf3307/dvmg15.pdf"> online</a>. <p> <li> M. Borovoi and J. van Hamel, <em> Extended Picard complexes and linear algebraic groups,</em> J. reine angew. Math. <strong>627</strong> (2009), 53-82, <a href="http://arxiv.org/abs/math/0612156"> arXiv:math/0612156</a>, <a href="http://www.reference-global.com/doi/pdf/10.1515/CRELLE.2009.011"> online</a>. <p> <li> M. Borovoi, <a href="http://www.math.u-psud.fr/~colliot"> J-L. Colliot-Th&eacute;l&egrave;ne</a> and <a href="http://www.ma.ic.ac.uk/~anskor">A.N. Skorobogatov</a>, <em>The elementary obstruction and homogeneous spaces,</em> Duke Math. J. <strong>141</strong> (2008), 321-364, <a href="http://arxiv.org/abs/math/0611700v2"> arXiv:math/0611700</a>, <a href="http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.dmj/1200601794">online</a>. <p> <li> M. Borovoi and J. van Hamel, <em>Extended Picard complexes for algebraic groups and homogeneous spaces,</em> C. R. Acad. Sci. Paris Ser I <strong>342</strong> (2006) 671-674, <a href="papers/CR-BvH.pdf">pdf</a>, <a href="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6X1B-4JKJT6M-2&_coverDate=05%2F01%2F2006&_alid=447863086&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=7238&_sort=d&view=c&_acct=C000005078&_version=1&_urlVersion=0&_userid=48161&md5=d2913222911daff1c76d4bafd90fa73f"> online</a>. <p> <li> T. Bandman, M. Borovoi, F. Grunewald, <a href="http://www.cs.biu.ac.il/~kunyav"> B. Kunyavskii</a> and E. Plotkin, <em>Engel-like characterization of radicals in finite dimensional Lie algebras and finite groups,</em> Manuscr. Math. <strong>119</strong> (2006) 365-381, <a href="papers/mm.pdf">pdf</a>, <a href="http://www.springerlink.com/content/e828mr3480ru61k2/">online</a>. <p> <LI> M. Borovoi and <a href="http://www.cs.biu.ac.il/~kunyav"> B. Kunyavskii,<a> with an appendix by P. Gille, <em>Arithmetical birational invariants of linear algebraic groups over two-dimensional geometric fields.</EM> J. of Algebra <strong>276</strong> (2004) 292-339, <a href="papers/bkG.pdf">pdf</a>, <a href="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WH2-4BJWWNJ-1&_coverDate=06%2F01%2F2004&_alid=447871869&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=6838&_sort=d&view=c&_acct=C000005078&_version=1&_urlVersion=0&_userid=48161&md5=d7ac961cca19170aed7d91a3fd8bb43f"> online</a>. <p> <LI> M. Borovoi, <EM>On representations of integers by indefinite ternary quadratic forms.</EM> J. of Number Theory <STRONG>90</STRONG> (2001), 281-293, <A HREF="papers/reprfin.pdf">pdf</a>, <a href="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WKD-457CHF3-K&_coverDate=10%2F31%2F2001&_alid=447875844&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=6904&_sort=d&view=c&_acct=C000005078&_version=1&_urlVersion=0&_userid=48161&md5=3b1451daa7da177419e7c3330754d966"> online</a>. <P> <LI> M. Borovoi and <a href="http://www.cs.biu.ac.il/~kunyav"> B. Kunyavskii,<a> <EM>Brauer equivalence in a homogeneous space with connected stabilizer.</EM> Michigan Math. J. <STRONG>49</STRONG> (2001), 197-205, <A HREF="papers/brauer.pdf">pdf</a>. <P> <LI> M. Borovoi and <a href="http://www.cs.biu.ac.il/~kunyav"> B. Kunyavskii,<a> <EM>Formulas for the unramified Brauer group of a principal homogeneous space of a linear algebraic group.</EM></A> J. Algebra <STRONG>225</STRONG> (2000), 804-821, <A HREF="papers/formulas.pdf">pdf</a>, <a href="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WH2-45F4R5V-BC&_coverDate=03%2F15%2F2000&_alid=447881061&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=6838&_sort=d&view=c&_acct=C000005078&_version=1&_urlVersion=0&_userid=48161&md5=1a1ab524a616c263ab94a34d5cf954fe"> online</a>. <P> <LI> M. Borovoi, <EM>The defect of weak approximation for homogeneous spaces.</EM></A> Ann. Fac. Sci. Toulouse <STRONG>8</STRONG> (1999), 219-233, <A HREF="papers/defect.pdf">pdf</a>, <a href="http://www.numdam.org/item?id=AFST_1999_6_8_2_219_0">online</a>. <P> <LI> M. Borovoi, <EM>A cohomological obstruction to the Hasse principle for homogeneous spaces.</EM></A> Math. Ann. <STRONG>314</STRONG> (1999), 491-504, <A HREF="papers/obstr.pdf">pdf</a>, <a href="http://www.springerlink.com/content/p3dm7d5y7m29cafp/"> online</a>. <P> <LI> M. Borovoi, <EM>Abelian Galois cohomology of reductive groups.</EM></A> Memoirs of the AMS <STRONG>132</STRONG> (1998), No. 626, 1-50, <A HREF="papers/galofile.pdf">pdf</a>. <P> <LI> M. Borovoi and <a href="http://www.cs.biu.ac.il/~kunyav"> B. Kunyavskii,<a> <EM>Spherical spaces for which the Hasse principle and weak approximation fail.</EM> Collect. Math. <STRONG>48</STRONG> (1997), 41-52, <A HREF="papers/sph.ps">ps</a>. <P> <LI> M. Borovoi, <EM>Abelianization of the first Galois cohomology of reductive groups.</EM> Internat. Math. Res. Not. 1996, 401-407, <a href="http://imrn.oxfordjournals.org/cgi/reprint/1996/8/401"> online</a>. <P> <LI> M. Borovoi, <EM>The Brauer-Manin obstruction to the Hasse principle for homogeneous spaces with connected or abelian stabilizer.</EM> J. reine angew. Math. <STRONG>473</STRONG> (1996), 181-194, <a href="papers/manin.pdf">pdf</a>, <a href="http://www.digizeitschriften.de/en/main/dms/img/?IDDOC=503406">online</a>. <P> <LI> M. Borovoi, <A HREF="http://www.math.tau.ac.il/~rudnick">Z. Rudnick,</A> <EM>Hardy-Littlewood varieties and semisimple groups.</EM> Invent. Math. <STRONG>119</STRONG> (1995), 37-66, <A HREF="papers/hardy.pdf">pdf</a>, <a href="http://www.springerlink.com/content/l1t0071152537186/"> online</a>. <P> <LI> M. Borovoi, <EM>Abelianization of the second nonabelian Galois cohomology.</EM> Duke Math. J. <STRONG>72</STRONG> (1993), 217-239, <a href="http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.dmj/1077289218"> online</a>. <P> <LI> M. Borovoi, <EM>The Hasse principle for homogeneous spaces.</EM> J. reine angew. Math. <STRONG>426</STRONG> (1992), 179-192. <P> <LI> M. Borovoi, <EM>On weak approximation in homogeneous spaces of simply connected algebraic groups.</EM> Proceedings of Internat. Conf. "Automorphic Functions and Their Applications, Khabarovsk, June 27-July 4, 1988" (N. Kuznetsov, V. Bykovsky, eds.) Khabarovsk, 1990, 64-81, <a href="papers/weak.pdf">scan</a>. <P> <LI> M. Borovoi, <EM>On weak approximation in homogeneous spaces of algebraic groups.</EM> Soviet Math. Doklady <STRONG>42</STRONG> (1991), 247-251. <P> <LI> M. Borovoi, <EM>On strong approximation for homogeneous spaces.</EM> Doklady Akad. Nauk BSSR <STRONG>33</STRONG> (1989), N4, 293-296 (Russian). <P> <LI> M. Borovoi, <EM>The abstract simplicity of groups of type D_n over number fields.</EM> Russian Math. Surveys <STRONG>43</STRONG> (1988), N5, 213-214. <P> <LI> M. Borovoi, <EM>Galois cohomology of real reductive groups, and real forms of simple Lie algebras.</EM> Functional. Anal. Appl. <STRONG>22</STRONG>:2 (1988), 135-136, online: <a href="http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=faa&paperid=1110&option_lang=rus">Russian</a>, <a href="http://www.springerlink.com/content/rm5h116227w12028/">English</a>. <P> <LI> M. Borovoi, <EM>On the group of points of a semisimple group over a real closed field.</EM> Voprosy Teorii Grupp i Gomologicheskoi Algebry, Yaroslavl (1987), 142-149 (Russian); English translation: Selecta Math. Soviet. <STRONG>9</STRONG> (1990), 331-338. <P> <LI> M. Borovoi, <EM>Conjugation of Shimura varieties.</EM> In:"Proc. Internat. Congr. Math., Berkeley, 1986", AMS, 1987, pp. 783-790. <P> <LI> M. Borovoi, <EM>Abstract simplicity of some simple anisotropic algebraic groups over number fields.</EM> Soviet Math. Doklady <STRONG>32</STRONG> (1985), N1, 191-193. <P> <LI> M. Borovoi, <EM>Generators and relations in compact Lie groups.</EM> Functional. Anal. Appl.<STRONG> 18</STRONG>:2 (1984), 133-135, online: <a href="http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=faa&paperid=1450&option_lang=rus">Russian</a>, <a href="http://www.springerlink.com/content/h80m87m793u82125/">English</a>. <P> <LI> M. Borovoi, <EM>Langlands' conjecture concerning conjugation of connected Shimura varieties.</EM> Selecta Math. Soviet. <STRONG> 3</STRONG> (1983-84), N1, 3-59. <P> <LI> M. Borovoi, <EM>The conjecture of Langlands on conjugation of Shimura varieties.</EM> Functional. Anal. Appl. <STRONG> 16</STRONG>:4 (1982), 292-294, online: <a href="http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=faa&paperid=1671&option_lang=rus">Russian</a>, <a href="http://www.springerlink.com/content/v472780r613p428n/">English</a>. <P> <LI> M. Borovoi, <EM>The Hodge group and the endomorphism algebra of an Abelian variety.</EM> Voprosy Teorii Grupp i Gomologicheskoi Algebry, Yaroslavl (1981), 124-126 (Russian). <P> <LI> M. Borovoi, <EM>The Shimura-Deligne schemes M(G,h) and the rational cohomology classes of type (p,p) of Abelian varieties.</EM> Voprosy Teorii Group i Gomologicheskoi Algebry, vyp. 1, Yaroslavl (1977), 3-53 (Russian). <P> <LI> M. Borovoi, <EM>The schemes M(G,h) and the Mumford-Tate group.</EM> Uspekhi Mat. Nauk <STRONG>32</STRONG> (1977),N6, 245-246 (Russian). <P> <LI> M. Borovoi, <EM>On the action of the Galois group on rational cohomology classes of type (p,p) of Abelian varieties.</EM> Mat. Sbornik <STRONG>94</STRONG> (1974), N4, 649-652 (Russian). </LI><P></P> </OL> <HR> <H2> Preprints </H2> <OL> <LI> M. Borovoi, <EM>Non-abelian hypercohomology of a group with coefficients in a crossed module, and Galois cohomology.</EM> Preprint, 1992, <A HREF="papers/nonab.pdf">pdf</a>. <p> </OL> <HR> <p> Last updated on August 21, 2013. <p> <p> . </BODY> </HTML>