Seminar
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| Location: | SLMath: Online/Virtual |
This seminar will focus on Diophantine problems in a broad sense, with a view towards (but not limited to) interactions between Number Theory and Logic. Particular attention will be given to topics with the potential of further developments in the context of this MSRI scientific program. This will provide an opportunity for researchers to update on new results, techniques and some of the main problems of the field.
To participate in this seminar, please register here: https://www.msri.org/seminars/25206
To participate in this seminar, please register here: https://www.msri.org/seminars/25206
Abstract: The CCT (Colliot-Thelene Conjecture) over a number field k is about giving birational conditions on morphisms of proper smooth k-varieties which imply surjectivity on the local rational points for almost all localization of k.
The CCT was proved in a stronger form by Denef (2017), and Loughran-Skorobogatov-Smeets (2019) gave necessary and sufficient conditions for Denef's result to hold. This talk (in some sense a follow-up to my 2019 Fields Institute talk) is about further generalizations of the afore mentioned results in several ways, by relaxing both the hypothesis on the bases field k, and the conditions on the varieties involved (e.g. no properness or smoothness, etc.). The point in my approach is to employ special forms of the AKE (whereas the CCT was—among other things—aimed at giving an arithmetic geometry proof of the AKE). I will also mention a few open questions and potential research directions.
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