Dr. Oliver Bräunling:
Around the residue symbol
Zeit und Ort
Donnerstag, 11.7.19, 16:15-17:15, Hörsaal II, Albertstr. 23b
Zusammenfassung
Everybody knows the “residue" from complex analysis and Cauchy's residue\nformula. One can regard this as a one-dimensional theorem in the sense\nthat the complex plane has complex dimension one. There are several\ndifferent theories of multi-dimensional residues, all essentially\ncompatible, but in complicated ways. I will explain a picture due to A.\nParshin.\nWhereas Cauchy's residue formula implies a statement of the form “the\nsum of residues at all points of a fixed curve is zero", Parshin's\n2-dimensional generalization provides a nice analogous result stating\nthat “the sum of residues along all curves passing through a fixed\npoint" is zero. This talk will focus on the down-to-earth geometric\napproach of the Soviet school to these issues, which is not so\nwell-known in the Western world.\n (I will not talk about the following, because it would be much too\ntechnical, but of course the same result also immediately follows from\nGrothendieck's residue symbol, the approach more popular in the Western\nworld, but only after introducing f!, derived categories, local\ncohomology, etc.; in fact Grothendieck's theory even in the classical\none-dimensional case already relies on local cohomology).