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Jared Weinstein. Reciprocity laws and Galois representations: recent breakthroughs
Given a polynomial f(x) with integer coefficients, a reciprocity law is a rule which determines, for a prime p, whether f(x) modulo p is the product of distinct linear factors. We examine reciprocity laws through the ages, beginning with Fermat, Euler and Gauss, and continuing through the modern theory of modular forms and Galois representations. We conclude with an exposition of Peter Scholze's astonishing work on torsion classes in the cohomology of arithmetic manifolds.
Jared Weinstein. Reciprocity laws and Galois representations: recent breakthroughs
Given a polynomial f(x) with integer coefficients, a reciprocity law is a rule which determines, for a prime p, whether f(x) modulo p is the product of distinct linear factors. We examine reciprocity laws through the ages, beginning with Fermat, Euler and Gauss, and continuing through the modern theory of modular forms and Galois representations. We conclude with an exposition of Peter Scholze's astonishing work on torsion classes in the cohomology of arithmetic manifolds.
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The gold standard of encryption, known as end-to-end encryption, where only the sender and person who receives the message are able to see it, is available on Telegram only when the Secret Chat function is enabled. Voice and video calls are also completely encrypted. He floated the idea of restricting the use of Telegram in Ukraine and Russia, a suggestion that was met with fierce opposition from users. Shortly after, Durov backed off the idea. Additionally, investors are often instructed to deposit monies into personal bank accounts of individuals who claim to represent a legitimate entity, and/or into an unrelated corporate account. To lend credence and to lure unsuspecting victims, perpetrators usually claim that their entity and/or the investment schemes are approved by financial authorities. "And that set off kind of a battle royale for control of the platform that Durov eventually lost," said Nathalie Maréchal of the Washington advocacy group Ranking Digital Rights. "We as Ukrainians believe that the truth is on our side, whether it's truth that you're proclaiming about the war and everything else, why would you want to hide it?," he said.
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