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Jinhyun Park, A Reciprocity Theorem Arising from a Family of Algebraic Curves

October 13 @ 11:00 am - 12:00 pm KST

B236-1, IBS
Korea, Republic of

     Speaker

Jinhyun Park
KAIST

The classical reciprocity theorem, also called the residue theorem, states that the sum of the residues of a rational (meromorphic) differential form on a compact Riemann surface is zero. Its generalization to smooth projective curves over a field is often called the Tate reciprocity theorem.

There is a different “multiplicative version” too. Here, instead of a rational form, one uses a pair of rational functions on a smooth projective curve, and instead of residues, one uses “Tame symbols”. The corresponding global result is called the Weil reciprocity. This result is elegantly reformulated in terms of the Milnor K-theory, and it is generalized to sequences of rational functions by A. Suslin. This Suslin reciprocity was recently strengthened by D. Rudenko, resolving a conjecture of A. Goncharov.

In this talk, let me sketch my recent work in-progress, that studies a different kind of reciprocity results coming from a proper family of algebraic curves over an algebraically closed field of characteristic 0.

Details

Date:
October 13
Time:
11:00 am - 12:00 pm KST
Event Category:
Event Tags:

Venue

B236-1
IBS
Korea, Republic of

Organizer

Jaehyun Hong
IBS 복소기하학연구단 Center for Complex Geometry
기초과학연구원 복소기하학연구단
대전 유성구 엑스포로 55 (우) 34126
IBS Center for Complex Geometry
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
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