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Catherine Hsu – University of Oregon
September 18, 2017 @ 4:30 pm - 5:30 pm
Higher Eisenstein Congruences
In this talk, we examine the relationship between the “depth” of certain Eisenstein congruences and the local structure of the Eisenstein ideal. Specifically, let be prime. For squarefree level and weight we use a commutative algebra result of Berger, Klosin, and Kramer to bound the depth of Eisenstein congruences modulo (from below) by the -adic valuation of the numerator of . We then show that if has at least three prime factors and some prime divides the Eisenstein ideal is not locally principal. Lastly, we illustrate these results with explicit computations and discuss generalizations to higher weights.