Regulator constants of integral representations

Alex Torzewski (University of Warwick)

Wednesday 15th November, 2017 16:00-17:00 Maths 311B


Regulator constants are numerical invariants of representations of finite groups. Whilst purely algebraic, they were inspired by the regulators which appear in arithmetic geometry. This link was exploited by Dokchitser-Dokchitser in their proof of the p-parity conjecture, an important piece of evidence for the Birch-Swinnerton-Dyer conjecture. In such applications, it is important to know how strong regulator constants are as invariants of representations.  For many groups with cyclic Sylow p-subgroup I have been able to show that regulator constants are good invariants of representations over Z_(p). This leads to an algorithm for determining such representations up to isomorphism. If time permits we may discuss a short application in the context of number fields.

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