IISER Mohali, Knowledge city, Sector 81, SAS Nagar, Manauli PO 140306

Explicit Reciprocity Laws in Number Theory

Prof Otmar Venjakob (Heidelberg University)

Location Online
Day and Time: 18 August, 2021 (Wednesday) , 4:30 PM (Indian Standard Time)/ 13:00 (CEST)

Abstract: The quadratic Reciprocity Law for the Legendre or Jacobi-Symbol forms the starting point of all Reciprocity Laws as well as of class field theory. It is closely related to the product formula of the quadratic Hilbert-Symbol over local fields. Various mathematicians have established higher explicit formulae to compute higher Hilbert-Symbols. Analogues were found for formal (Lubin-Tate) groups. Eventually Perrin-Riou has formulated a Reciprocity Law, which allows the explicit computation of local cup product pairings by means of Iwasawa- and p-adic Hodge Theory. In this talk I shall try to give an overview of these topics, at the end I will explain recent developments in this regard.

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Meeting ID: 945 6317 7769
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