Forschungsseminar über Motive-WS 2014/15

Meeting time and place:

We meet on Tuesdays,14-16 Uhr (c.t.), in WSC-N-U-4.04

Program

This semester we will hold a seminar on elliptic motives. Here is an preliminary outline:

1. Beiinson's conjectures 6 lectures

2. Polylogarithm and elliptic polylogarithm 3 lectures

3. Elliptic multipolylog.  2 lectures 

4. Multiple Modular values. 2 lectures

 

Schedule

Part 1: Beilinson's conjectures

28.10.2014-Adeel Kahn, "Beilinson-Deligne cohomology" [BR] sec. 1

4.11.2014-Federico Binda, "Regulators and arithmetic intersection", [BR] sec. 2

11.11.2014-Ishai Dan-Cohen, "Beilinson's conjectures", [BR] sec. 3

18.11.2014-Giuseppe Ancona, "Regulators of modular curves, 1" [BM]

25.11.2014-Jin Cao,  "Regulators of modular curves, 2" [BM]

2.12.2014-Lorenzo Mantovani,  "Regulators of modular curves, 3" [BM]

Part 2: Polylogarithm and elliptic polylogarithm

9.12.2014-Rin Sugayama, "Motivic polylogarithm" [BD]

16.12.2014-Matthias Wendt, "Elliptic polylog, 1" [BL]

13.1.2015-Toan Nguyen, "Elliptic polylog, 2" [BL]

Part 3: Elliptic multipolylog

20.1.2015-Thomas Poguntke, "Multiple elliptic polylog, 1" [BrL]

27.1.2015-Gabriela Guzman, "Multiple elliptic polylog, 2" [BrL]

Part 4: Multiple modular values

3.2.2-15-Girja Tripathi, "Multiple Modular Values, 1" [Br]

10.2.2015-Marc Levine,  "Multiple Modular Values, 2" [Br]

 

Bibliography

[BR] A. Beilinson, "Higher regulators and values of L-fucntions"

[BM] A. Beilinson, "Higher regulators of modular curves"

[BD] A. Beilinson, P. Deligne, "Interprétation motivique de la conjecture de Zagier reliant polylogarithmes et régulateurs. Motives (Seattle, WA, 1991), 97–121, Proc. Sympos. Pure Math., 55, Part 2, Amer. Math. Soc., Providence, RI, 1994.

[BeL] A. Beilinson, A. Levin, "Elliptic polylogarithm"

[BrL] F. Brown, A. Levin, "Multiple Elliptic Polylogarithms" arXiv:1110.6917 [math.NT] Francis C. S. Brown, Andrey Levin 

[Br] F. Brown "Multiple Modular Values for SL₂(Z)" arXiv:1407.5167 [math.NT]

"Beilinson's conjectures on special values of L-functions". Edited by M. Rapoport, N. Schappacher and P. Schneider. Perspectives in Mathematics, 4. Academic Press, Inc., Boston, MA, 1988.

Nekovár, Jan "Beilinson's conjectures". Motives (Seattle, WA, 1991), 537–570, Proc. Sympos. Pure Math., 55, Part 1, Amer. Math. Soc., Providence, RI, 1994.

Beilinson, A. A. "Notes on absolute Hodge cohomology". Applications of algebraic K-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983), 35–68, Contemp. Math., 55, Amer. Math. Soc., Providence, RI, 1986.

Beilinson, A. "Height pairing between algebraic cycles". Current trends in arithmetical algebraic geometry (Arcata, Calif., 1985), 1–24, Contemp. Math., 67, Amer. Math. Soc., Providence, RI, 1987.