Number Theory Seminar : Wednesday: 12/04/2023, 2.30 pm

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Host: Preeti Raman : Venue: Room 216

Speaker: Parul Gupta : Affiliation: IISER, Pune

Title: A ruled residue theorem for function fields of elliptic curves

Abstract: Let E be a field and v be a valuation on E. The ruled residue theorem, proved by J. Ohm in 1983, characterizes residue field extensions for valuations on a rational function field E(X) in one variable. It states that for any extension of v from E to E(X), the corresponding field extension at the level of residue fields is either algebraic or ruled, i.e., it is a rational function field in one variable over a finite extension of the residue field of E. In this talk, we will discuss residue field extensions for valuation extensions of v to the function field F of an elliptic curve over E. In this case, we show that there exists at most one extension of v to F such that the corresponding residue field extension is neither algebraic nor ruled. We also describe the cases where such an extension occurs. This is joint work with K. J. Becher and S. Mishra.

Algebraic Geometry seminar

Wednesday, 12th April 2023 at 4 pm

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Host: Madhusudan Manjunath 

Venue: Room 215

Speaker: Saurav Bhaumik, IIT Bombay

Title: The Hard Lefschetz Theorem

Abstract: We will state and prove the hard Lefschetz theorem.