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College of Liberal Arts and Sciences | Mathematics

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February 19, 2019 | 3:00 p.m. - 4:00 p.m.
Category: Seminar
Location: Faculty/Administration #1140 | Map
656 W. Kirby
Detroit, MI 48202
Cost: Free

Speaker: Wayne Raskind, Wayne State University

Title: Cohomology of algebraic varieties over the maximal cyclotomic extension of global fields (Part 2)

Abstract:

In these talks, I will review basic facts about the cohomology of algebraic varieties, especially surfaces, defined over various types of fields such as the complex numbers, p-adic fields, finite fields and algebraic number fields. The conjectures of Hodge and Tate predict what part of the even degree cohomology is generated by the classes of algebraic cycles. In the second talk, I will review a well-known theorem of Ribet on finiteness of torsion of abelian varieties over the maximal cyclotomic extension of a number field, which is obtained by adjoining all roots of unity, and generalizations for odd-dimensional cohomology by Roessler-Szamuely. Finally, I will present a counterexample for even dimensional cohomology of the function field analogue of these results.

For more information about this event, please contact Department of Mathematics at 3135772479 or math@wayne.edu.