Seminars this semester


   Series:


Feb 7 Thu Masahiro Nakahara (Manchester)
14:00 J11 Index of Fibrations and Brauer classes that never obstruct the Hasse principle
 
  Abstract:
Let X be a smooth projective variety over a number field with a fibration into varieties that satisfy a certain condition. We study the classes in the Brauer group of X that never obstruct the Hasse principle for X. We prove that if the generic fiber has a zero-cycle of degree d over the generic point, then the Brauer classes whose orders are prime to d do not play a role in the Brauer-Manin obstruction. As a result we show that the odd torsion Brauer classes never obstruct the Hasse principle for del Pezzo surfaces of degree 2, certain K3 surfaces, and Kummer varieties.
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Mar 7 Thu Jean-Stefan Koskivirta (Tokyo)
14:00 J11 Ampleness and vanishing results
 
  Abstract:
We explain an application of the existence of generalized Hasse invariants to show ampleness of certain line bundles on flag spaces of Shimura varieties of Hodge type in positive characteristic. These methods generalize to other types of schemes which carry a universal G-zip. We deduce vanishing results for the cohomology of automorphic vector bundles. We compare them with similar results of Lan-Suh.
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Mar 21 Thu Tom Fisher (Cambridge)
14:00 J11 The proportion of genus one curves that are everywhere locally soluble
 
  Abstract:
I will describe joint work with Bhargava and Cremona, and with Ho and Park, on the probability that a randomly chosen genus one curve is soluble over the p-adics. A striking feature of this work is that we obtain exact answers in the form of explicit rational functions of p. I will also discuss what is expected to happen globally.
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Apr 4 Thu Chris Birkbeck (UCL)
14:00 J11 TBA
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