COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Number Theory Seminar > A class number formula for Picard modular surfaces

## A class number formula for Picard modular surfacesAdd to your list(s) Download to your calendar using vCal - Shrenik Shah (Columbia University)
- Tuesday 30 May 2017, 15:30-16:30
- MR13.
If you have a question about this talk, please contact G. Rosso. The original class number formula of Dirichlet connected the residue of the Dedekind zeta function of a number field at s=1 to various arithmetic invariants of the number field, including a transcendental quantity called the regulator, which measures the covolume of a lattice generated by logarithms of units. Beilinson formulated a conjectural generalization of this formula, again connecting a regulator, defined in terms of “higher” units, to the special value of a “motivic” L-function. We study a particular case of this conjecture, namely for the motive of the middle degree cohomology of the smooth compactified Picard modular surfaces X attached to the unitary group GU(2,1) for an imaginary quadratic extension E/Q. We will concretely describe a construction of suitable elements in the motivic cohomology H_M^3(X,Q(2)). We then explain how to compute their regulator as an element of Deligne cohomology by interpreting this map via the pairing of these classes against automorphic differential forms, and show that the regulator is non-vanishing when predicted. As a consequence, we obtain a higher “class number formula” involving a non-critical L-value of the degree 6 Standard L-function, a Whittaker period, and the regulator. One interesting aspect of this work is that we must account for endoscopic forms via a period, which is predicted by the conjecture. This is joint work with Aaron Pollack. This talk is part of the Number Theory Seminar series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- Hanchen DaDaDash
- Interested Talks
- MR13
- Number Theory Seminar
- School of Physical Sciences
- bld31
Note that ex-directory lists are not shown. |
## Other listsCancer Genetic Epidemiology Seminar Series Faraday Institute Clinical Science Seminars Cambridge Interdisciplinary Reproduction Forum Horizon: A Sensory World. Novel Sensor Technologies and Applications Associative experiment## Other talksSmall Opuntioideae Quantifying Uncertainty in Turbulent Flow Predictions based on RANS/LES Closures Respiratory Problems Smuts, bunts and ergots Prof Murray Shanahan: Artificial Intelligence Ethics for the working mathematician, seminar 9 CANCELLED |