Recent Publications and Preprints

by Alexander Merkurjev


 
Merkurjev A.
Divisible abelian Brauer groups
Doc. Math., Extra volume (2015), 461-462 (electronic).
                                         
Merkurjev A., Tignol J.-P.
Excellence of function fields of conics
                                         
Merkurjev A.
Cohomological invariants of central simple algebras
                                         
Laackman D., Merkurjev A.
Degree three cohomological invariants of reductive groups
                                         
Merkurjev A.
Invariants of algebraic groups and retract rationality of classifying spaces
                                         
Merkurjev A.
Essential Dimension
Bourbaki talk, June 27, 2015.
                                         
Merkurjev A.
Unramified degree three invariants of reductive groups
to appear in Advances in Mathematics.
                                         
Merkurjev A.
Motivic decomposition of certain special linear groups
To appear in Transactions of the AMS.
                                         
Karpenko N., Merkurjev A.
Motivic decomposition of compactifications of certain group varieties
To appear in Crelle.
                                         
Merkurjev A., Neshitov A., Zainoulline K.
Invariants of degree 3 and torsion in the Chow group of a versal flag
Compositio Mathematica, 151 (2015), no. 12, 1416-1432.
                                         
Karpenko N., Merkurjev A.
Hermitian forms over quaternion algebras
Compositio Mathematica, 150 (2014), no. 12, 2073-2094.
                                         
Merkurjev A.
Degree three cohomological invariants of semisimple groups
J. Eur. Math. Soc. (JEMS), 18 (2016), no. 2, 657-680.
                                         
Merkurjev A.
Weight two motivic cohomology of classifying spaces for semisimple groups
To appear in AJM.
                                         
Merkurjev A.
On the Chow group of cycles of codimension 2
                                         
Merkurjev A.
Essential dimension: a survey
Transformation Groups, 18, no. 2, (2013), 415-481.
                                         
Blinstein S., Merkurjev A.
Cohomological invariants of algebraic tori
Algebra & Number Theory, 7 (2013), no. 7, 1643-1684.
                                         
Merkurjev A.
Essential dimension of certain subfunctors
                                         
Karpenko N., Merkurjev A.
On standard norm varieties
Ann. Sci. Ecole Norm. Sup., 4-e serie, 46 (2013), no. 8, 175-214.
                                         
Chernousov V., Merkurjev A.
Essential dimension of Spinor and Clifford groups
Algebra & Number Theory, 2 (2014), no. 1, 457-472.
                                         
Merkurjev A.
Developments in Algebraic K-Theory and Quadratic Forms After the Work of Milnor
Collected papers of John Milnor, V: Algebra, 2010, 399-418.
                                         
Chernousov V., Merkurjev A.
Essential p-dimension of split simple groups of type A_n
Mathematische Annalen, 357 (2013), no. 1, 1--10.
                                         
Baek S., Merkurjev A.
Essential dimension of central simple algebras
Acta Mathematica, 209 (2012), no. 1, 127
                                         
Merkurjev A.
A lower bound on the essential dimension of simple algebras
Algebra & Number Theory, 4 (2010), no. 8, 1055-1076.
                                         
Merkurjev A.
Periods of principal homogeneous spaces of algebraic tori
Vestnik St. Petersburg University, Mathematics, 43 (2010), no. 1, 39-43.
                                         
Merkurjev A.
Adams operations and the Brown-Gersten-Quillen spectral sequence
Quadratic forms, linear algebraic groups, and cohomology, Dev. Math., 18, Springer, New York (2010), 305313.
                                         
Merkurjev A.
Zero-cycles on algebraic tori
Geometry of algebraic cycles, Proceedings of the Conference on algebraic cycles March 25-29, 2008, Ohio State University, Clay Mathematical Proceedings, v. 9, 2010, 119-123
                                         
Merkurjev A., Suslin A.
Motivic cohomology of the simplicial motive of a Rost variety
Journal of Pure and Applied Algebra, 214 (2010), 2017-2026.
                                         
Baek S., Merkurjev A.
Invariants of simple algebras
Manuscripta Math., 129 (2009), no. 4, 409-421.
                                         
Merkurjev A.
Essential p-dimension of PGL(p^2)
J. Amer. Math. Soc., 23 (2010), 693-712.
                                         
Elman R., Karpenko N., Merkurjev A.
The algebraic and geometric theory of quadratic forms
American Mathematical Society Colloquium Publications, 56. American Mathematical Society, Providence, RI, 2008. 
                                   
Merkurjev A.
Essential p-dimension of finite groups
Notes of mini-course in Lens, June 2008.
                                         
Merkurjev A.
Essential dimension
Proceedings of the International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms, Frutillar, Chile, December 13-19, 2007, Contemp. Math., 493, Amer. Math. Soc., Providence, R.I., 2009, 299-325.
                                         
Karpenko N., Merkurjev A.
Essential dimension of finite p-groups
Invent. Math., 172 (2008), no. 3, 491--508.
                                         
Merkurjev A.
$R$-equivalence on $3$-dimensional tori and zero-cycles
Algebra & Number Theory, 2 (2008), no. 1, 69--90.
                                         
Merkurjev A.
Unramified elements in cycle modules
J. London Math. Soc., 78 (2008), 51-64.
                                         
Colliot-Thelene J-L., Karpenko, N., Merkurjev A.
Rational surfaces and canonical dimension of PGL6
Algebra i Analiz, 19 (2007), no. 5, 159--178, translation in St.Petersburg Math.J. 19 (2008), no. 5, 793--804.
                                         
Merkurjev A., Suslin A.
The group of K1-zero-cycles on Severi-Brauer varieties
J. Nova Journal of Algebra and Geometry, 1, no. 3 (1992), 297-315.
                                         
Chernousov V., Merkurjev A.
Connectedness of classes of fields and zero cycles on projective homogeneous varieties
Compositio Mathematica, 142 (2006), no. 6, 15221548.
                                         
Karpenko N., Merkurjev A.
Canonical p-dimension of algebraic groups
Adv. Math. 205 (2006), no. 2, 410-433.
                                         
Merkurjev A.
Algebraic Cobordism Theory
Notes of mini-course in Lens, June 2004.
                                         
Chernousov V., Merkurjev A.
Motivic decomposition of projective homogeneous varieties and the Krull-Schmidt theorem
Transformation Groups, 11, no. 3, (2006), 371-386.
                                         
Merkurjev A.
On the norm residue homomorphism of degree two
Proceedings of the St. Petersburg Mathematical Society. Vol. XII, Amer. Math. Soc. Transl. Ser. 2, 219, 103-124, American Mathematical Society, Providence, 2006.
                                         
Merkurjev A.
SK1 for degree 4 simple algebras
$K$-Theory, 37 (2006), 311-319.
                                         
Garibaldi S., Merkurjev A., Serre J-P.
Cohomological Invariants in Galois Cohomology
American Mathematical Society University Lecture Series, 28. American Mathematical Society, Providence, RI, 2003.
                                         
Merkurjev A.
Steenrod operations in algebraic geometry
Notes of mini-course in Lens, June 2003.
                                         
Merkurjev A.
Rational correspondences
                                        
Chernousov V., Gille S., Merkurjev A.
Motivic decomposition of isotropic projective homogeneous varieties
Duke Math. J.. Vol. 126, 2005, 137--159.
                                        
Merkurjev A.
Equivariant K-theory
J. Handbook of $K$-theory. Vol. 1, 2, Springer, Berlin, 925-954, 2005.
                                        
Merkurjev A.
Steenrod operations and degree formulas
J. Reine Angew. Math. 565, 2003, 13-26.
                                        
Karpenko N., Merkurjev A.
Rost projectors and Steenrod operations
Doc. Math., 7 (2002), 481-493 (electronic).
                                        
Karpenko N., Merkurjev A.
Essential dimension of quadrics
Invent. Math., 153 (2003), no. 2, 361-372.
                                        
Merkurjev A.
Algebraic oriented cohomology theories
Algebraic Number Theory and Algebraic Geometry, 171-194, Contemp. Math., 300, Amer. Math. Soc., Providence, R.I., 2002.
                                         
Merkurjev A.
Rost's degree formula
Notes of mini-course in Lens, June 2001.
                                         
Merkurjev A., Parimala R., Tignol J.-P.
Invariants of quasi-trivial tori and the Rost invariant
Algebra i Analiz, 14 (2002), no. 5, 110-151, translation in St.Petersburg Math.J. 14 (2003), no. 5, 791-821.
                                         
Merkurjev A.
Unramified cohomology of classifying varieties for classical simply connected groups
J. Ann. Sci. Ecole Norm. Sup., 4-e serie, 35 (2002), 445-476.
                                                         
Barquero P., Merkurjev A.
Norm Principle for Reductive Algebraic Groups
J. Proceedings of the International Colloquium on Algebra, Arithmetic and Geometry TIFR, Mumbai, January 4-12, 2000.
                                        
Chernousov V., Merkurjev A.
R-equivalence in spinor groups
J. Amer. Math. Soc., 14 (2001), 509-534.
                                    
Merkurjev A.
Cohomological invariants of simply connected groups of rank 3
Journal of Algebra, 227 (2000), no. 2 , 614-632. 
                                   
Merkurjev A.
Invariants of algebraic groups
J. Reine Angew. Math., 508 (1999), 127-156.