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Tag Archives: Grothendieck
The paramodular conjecture is false for trivial reasons
(This is part of a series of occasional posts discussing results and observations in my joint paper with Boxer, Gee, and Pilloni mentioned here.) Brumer and Kramer made a conjecture positing a bijection between isogeny classes of abelian surfaces over … Continue reading
The ABC conjecture has (still) not been proved
The ABC conjecture has (still) not been proved. Five years ago, Cathy O’Neil laid out a perfectly cogent case for why the (at that point recent) claims by Shinichi Mochizuki should not (yet) be regarded as constituting a proof of … Continue reading
Effective Motives
This is a brief follow up concerning a question asked by Felipe. Suppose we assume the standard conjectures. Let be a pure motive, and consider the following problems: Problem A: (“effectivity”) Suppose that has nonnegative HodgeTate weights. Then is effective? … Continue reading
Posted in Mathematics
Tagged Deligne, Farbster, Grothendieck, Motives, Standard Conjectures
5 Comments
The Two Cultures of Mathematics: A Rebuttal
Gowers writes thoughtfully about combinatorics here, in an essay which references Snow’s famous lectures (or famous amongst mathematicians – I’ve never met anyone else who has ever heard of them). The trouble, however, starts (as it often does) with the … Continue reading