# Upcoming Talks

The seminar will meet at 4:30 on Monday in 2-131 unless otherwise noted.

http://math.mit.edu/topology/topology_seminar.ics

• Dec 102018

### Irina Bobkova (Institute for Advanced Study)

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#### Invertible $E_2^{hC_4}$-modules

For Morava $E$-theory $E_n$ and a finite subgroup $F$ of the Morava stabilizer group, the spectrum $E_n^{hF}$ is periodic and the Picard group of the category of modules over the ring spectrum $E_n^{hF}$ contains the cyclic subgroup generated by $\Sigma E_n^{hF}$. In most known examples, the Picard group is found to be precisely this cyclic group. However, at chromatic height $n=2$ and $p=2$, the Picard group of the category of $E_2^{hC_4}$-modules is not cyclic and contains an extra element of order 2. I will describe the tools we use to compute this Picard group: a group homomorphism from $RO(C_4)$ to it and the Picard spectral sequence. This talk is based on joint work with Agnes Beaudry, Mike Hill and Vesna Stojanoska.

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