15-17 Jan, 2008 at IMSc, Chennai

Oraganiser: Jaya NN Iyer (IMSc)

There will be a 3-day mini-workshop on K-theory and algebraic cycles at IMSc, Chennai between 15-17 Jan 2008 (arrival 14 Jan evening and departure 18 Jan).

Confirmed speakers:

Chuck Weibel (Rutgers University)

Dinakar Ramakrishnan (Caltech)

Joseph Ayoub (University of Paris-6)

Minhyong Kim (University College, London)

R. Sujatha (Tata Institute, Mumbai)

Donu Arapura (Purdue University)

Uwe Jannsen (University of Regensburg)

Andrea Miller (Harvard University)

Kapil Paranjape (IMSc, Chennai)

Ramesh Sreekantan (Tata Institute, Mumbai)

G.V. Ravindra (IISc, Bangalore)

Jishnu Biswas (ISI, Bangalore)

Schedule of talks

Reaching IMSc

There will be a lecture session in the mornings, with an emphasis on introductory talks for the non-specialists and a discussion meeting in the afternoons, led by an expert.

J. Ayoub (2 talks): Chow groups and motivic cohomology

R. Sujatha (2 talks): Introduction to Chow motives and Standard conjectures.

M. Kim: The motivic fundamental group and Diophantine geometry

D. Arapura: Hodge Conjecture

U. Jannsen: Varieties defined over finite fields.

The idea would be to talk about the Tate conjecture and the results in this setting, as well as the more general conjectures and results about motivic cohomology and l-adic cohomology in this setting. As for the results, I could mention some results in my paper "On finite-dimensional motives and Murre's conjecture" which appeared in the proceedings of the conference in honour of Murre.

Suggested reading/reference:

1. A.J. Scholl: Classical motives, Motives (Seattle, WA, 1991), 163-187, Proc.Sympos.Pure Math., 55, Part 1, Amer.Math.Soc., Providence, RI, 1994.

2. S.L. Kleiman: Motives. Algebraic geometry, Oslo 1970 (Proc. Fifth Nordic Summer-School in Math., Oslo, 1970), pp. 53--82. Wolters-Noordhoff, Groningen, 1972.

3. S.L. Kleiman: The standard conjectures. Motives (Seattle, WA, 1991), 3--20, Proc. Sympos. Pure Math., 55, Part 1, Amer. Math. Soc., Providence, RI, 1994.

4. Y. André: Une introduction aux motifs (motifs purs, motifs mixtes, périodes). (French) [An introduction to motives (pure motives, mixed motives, periods)] Panoramas et Synthèses [Panoramas and Syntheses], 17. Société Mathématique de France, Paris, 2004. xii+261 p.

5. M. Green, J. Murre, C. Voisin: Algebraic cycles and Hodge theory. Lectures given at the Second C.I.M.E. Session held in Torino, June 21--29, 1993. Edited by A. Albano and F. Bardelli. Lecture Notes in Mathematics, 1594. Springer-Verlag, Berlin, 1994. viii+275 pp.

6. J. Lewis: Three lectures on the Hodge conjecture. Transcendental aspects of algebraic cycles, 199--234, London Math. Soc. Lecture Note Ser., 313, Cambridge Univ. Press, Cambridge, 2004.

7. J. Lewis: A survey of the Hodge conjecture. Second edition. Appendix B by B. Brent Gordon. CRM Monograph Series, 10. American Mathematical Society, Providence, RI, 1999. xvi+368 pp.

8. D. Arapura: Motivation for Hodge cycles, Advances of Math vol 207 (2006).

9. U. Jannsen: On finite-dimensional motives and Murre's conjecture, appeared in the proceedings of the conference in honour of Murre.

10. M. Kim: The motivic fundamental group of $\bold P\sp 1\sbs\{0,1,\infty\}$ and the theorem of Siegel. Invent. Math. 161 (2005), no. 3, 629--656.

11. Deligne, P. Le groupe fondamental de la droite projective moins trois points. Galois groups over $Q$ (Berkeley, CA, 1987), 79--297, Math. Sci. Res. Inst. Publ., 16, Springer, New York, 1989.

You may also look at C. Weibel's notes at his homepage:

1. The development of Algebraic K-theory before 1980.

2. A Road Map of Motivic Homotopy and Homology Theory . pp. 385-392 in New Contexts for Stable Homotopy Theory, NATO ASI Series II, no.131, Kluwer Press, 2004.

3. Review of Cycles, Motives and Motivic Homology Theories , Bull. AMS 39 (2002), 137-143.

4. The K-book: An introduction to Algebraic K-theory.

5. Lectures on Motivic Cohomology.

If you would like to attend this meeting, please register by sending an email to jniyer AT imsc DOT res DOT in .

Deadline for request for accomodation: 14 Dec 2007.

Accomodation and boarding will be provided to selected participants and travel expenses may be provided to out-station participants.