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.
BY Непрерывное математическое образование
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Two days after Russia invaded Ukraine, an account on the Telegram messaging platform posing as President Volodymyr Zelenskiy urged his armed forces to surrender. In a statement, the regulator said the search and seizure operation was carried out against seven individuals and one corporate entity at multiple locations in Ahmedabad and Bhavnagar in Gujarat, Neemuch in Madhya Pradesh, Delhi, and Mumbai. In a message on his Telegram channel recently recounting the episode, Durov wrote: "I lost my company and my home, but would do it again – without hesitation." The War on Fakes channel has repeatedly attempted to push conspiracies that footage from Ukraine is somehow being falsified. One post on the channel from February 24 claimed without evidence that a widely viewed photo of a Ukrainian woman injured in an airstrike in the city of Chuhuiv was doctored and that the woman was seen in a different photo days later without injuries. The post, which has over 600,000 views, also baselessly claimed that the woman's blood was actually makeup or grape juice. In 2018, Russia banned Telegram although it reversed the prohibition two years later.
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