Publications, preprints and lecture notes
Return to Marc Levine's home page

Lecture Notes:

JAMI 2009: Tate motives and fundamental groups, March 25, 2009.

UCLA Colloquium: a survey of algebraic cobordism, Jan. 22, 2009.

BU Conference on motives QFT and pseudo-differential operators, June 2008
Lecture 1 Cycle complexes
Lecture 2 Motivic categories
Lecture 3 Tate motives.

ICTP school on algebraic K-theory and its applications, May 2007.
Six lectures on motives

French-Asian summer school in algebraic geometry and number theory, I.H.E.S. July 2006.
Six lectures on motives

Conference on Motives and Algebraic Cycles, in honor of Spencer Bloch,
Fields Institute-March 19-23, 2007
Motivic Postnikov towers
A lecture on Voevodsky's slice filtration, its relation to the homotopy coniveau tower,
with some applications to Severi-Brauer varieties and central simple algebras.

2nd German-Chinese conference on complex geometry, Shanghai-Sept. 2006
Algebraic cobordism
A lecture on algebraic cobordism, including a discussion of ``double-point" cobordism
and an application to Donaldson-Thomas invariants.

Three lectures on algebraic cobordism
Motives and Periods, June 5-12, 2006
UBC, Vancouver
Lecture 1, Lecture 2, Lecture 3

Introduction to algebraic cobordism
The first of 3 lectures on algebraic cobordism in the Distinguished Lecture Series
of the University of Western Ontario Mathematics Department,
Jan. 25-27, 2005.

A summer course in motivic homotopy theory
Algebraic geometry background, Nordfjordeid, 2003

A short course in K-theory
Morelia, 2002


Smooth Motives
Preprint (2008)

Comparison of cobordism theories
Preprint (2008)

Oriented cohomology, Borel-Moore homology and algebraic cobordism
Preprint (2008)

(with Bruno Kahn) Motives of Azumaya algebras
Preprint (2007)

(with Hélène Esnault) Tate motives and the fundamental group
Preprint (2007)

(with Amalendu Krishna) Additive higher Chow groups of schemes
Preprint (2006)

(with Rahul Pandharipande) Algebraic Cobordism Revisited
Preprint (2006)

(with Fabien Morel) Algebraic Cobordism
(2006). This is a manuscript for a book on algebraic cobordism,
essentially an assembly and revision of Algebraic Cobordism I
and Algebraic Cobordism II, with additional constructions and results.

Chow's moving lemma in A1 homotopy theory
revised version (2006)

Motivic Tubular Neighborhoods
Preprint (2005)

The homotopy coniveau filtration
revised version (2005)

(with C. Serpe') On a spectral sequence for equivariant K-theory
Preprint (2005)

Steenrod operations, degree formulas and algebraic cobordism
Preprint (2005)

Chow's moving lemma in A1 homotopy theory
Preprint (2004)

K-theory and motivic cohomology of schemes, I
Preprint (2004)

The homotopy coniveau filtration
Preprint (2003)

(with F. Morel) Algebraic cobordism, I
Preprint (2002), revised version.

Algebraic cobordism, II
Preprint (2002)

Selected Publications:

Mixed Motives
An expository article in the Handbook of K-theory, vol 1,
E.M. Friedlander, D.R. Grayson, eds.,
429-522. Springer Verlag, 2005.

A survey of algebraic cobordism
Proceedings of the International Conference on Algebra.
Algebra Colloq. 11 (2004), no. 1, 79--90.

(with S. Bloch and H. Esnault)   Divisibility of the eigenvalues of
Frobenius acting on étale cohomology of singular projective varieties

Amer. J. Math. 127 (2005), no. 1, 193--207.

Fundamental classes in algebraic cobordism
K-Theory 30 (2) (2003), 129-135.

Algebraic cobordism
Proceedings of the 2002 ICM, August, 2002.

(with F. Morel)  Cobordisme algébrique, I
C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), no. 8, 723--728.

(with F. Morel)  Cobordisme algébrique, II
C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), no. 9, 815--820.

Techniques of localization in the theory of algebraic cycles
J. Alg. Geom. 10 (2001) 299-363.

Blowing up monomial ideals
JPAA  160 (2001) 67-103.

(with T. Geisser)  The Bloch-Kato conjecture and a theorem of

Jour. f.d. Reine u. Ang. Math 530 (2001), 55-103.

Inverting the motivic Bott element
K-Theory  19 (2000), no. 1, 1--28.

(with H. Esnault)  The Steinberg curve
Amer. J. Math. 122 (2000), no. 4, 783--804

(with T. Geisser)  The K-theory of fields in characteristic p
Invent. Math. 139 (2000), no. 3, 459--493.

Mixed Motives    On-line version
Math. Surveys and Monographs 57, x+515 pp., AMS, Prov. 1998.

(with H. Esnault, B. Kahn, E. Viehweg)
The Arason invariant and mod 2 algebraic cycles
J. of the AMS, 11 no. 1, (1998), 73-118.

Homology of algebraic varieties: an introduction
to the works of Suslin and Voevodsky

Bull. Amer. Math. Soc. (N.S.)  34 (1997), no. 3, 293-312.

Lambda operations, K-theory and motivic cohomology
Algebraic K-Theory, (volume in memory of R. Thomason)
ed. V. Snaith, Fields Inst. Communications 16 (1997) 131-184.

(with H. Esnault, E. Viehweg)
Chow groups of projective varieties of very small degree
Duke Math. J. 87 (1997), no. 1, 29-58.

The weight two K-theory of fields
K-theory 9 No. 5, (1995) 443-501.

Bloch's higher Chow groups revisited
K-theory Strasbourg 1992 Astérisque vol. 226,
ed. C. Kassel, J.L. Loday, N. Schappacher,
Soc. Math. de France(1994) 235-320.

(with H. Esnault)  Surjectivity of cycle maps
Journées de Geométrie Algébrique D'Orsay, Juillet 1992,
Astérisque vol.  218(1993) 203-226.

Tate motives and the vanishing conjectures for algebraic K-theory
Algebraic K-Theory and Algebraic Topology,
ed. P.G. Goerss and J.F. Jardine,
NATO ASI Series, Series C, Vol. 407 (1993) 167-188.

Note: These publications are in the form of the final revised manuscript, before any
final correction of page-proofs. For the finished version, please check the actual journal

Last modified: February 15, 2010