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Recent progress on Zagier’s conjecture and Goncharov’s program (after Goncharov, Rudenko, Gangl,...). (English) Zbl 07554183

Séminaire Bourbaki. Volume 2019/2021. Exposés 1166–1180. Avec table par noms d’auteurs de 1948/49 à 2019/21. Paris: Société Mathématique de France (SMF). Astérisque 430, 295-343, Exp. No. 1176 (2021).
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Cohomological methods in intersection theory. (English) Zbl 1478.14003

Neumann, Frank (ed.) et al., Homotopy theory and arithmetic geometry – motivic and Diophantine aspects. LMS-CMI research school, London, UK, July 9–13, 2018. Lecture notes. Cham: Springer. Lect. Notes Math. 2292, 49-105 (2021).
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Homotopy theory and arithmetic geometry – motivic and Diophantine aspects: an introduction. (English) Zbl 1478.14004

Neumann, Frank (ed.) et al., Homotopy theory and arithmetic geometry – motivic and Diophantine aspects. LMS-CMI research school, London, UK, July 9–13, 2018. Lecture notes. Cham: Springer. Lect. Notes Math. 2292, 1-9 (2021).
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Syntomic regulators of Asai-Flach classes. (English) Zbl 1470.11107

Kurihara, Masato (ed.) et al., Development of Iwasawa theory – the centennial of K. Iwasawa’s birth. Proceedings of the international conference “Iwasawa 2017”, University of Tokyo, Tokyo, Japan, July 19–28, 2017. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 86, 595-638 (2020).
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The companions conjecture [after Deligne, Drinfeld, L. Lafforgue, T. Abe, …]. (La conjecture des compagnons [d’aprés Deligne, Drinfeld, L. Lafforgue, T. Abe, …].) (French) Zbl 1466.14023

Séminaire Bourbaki. Volume 2018/2019, Exposés 1151–1165. Avec table par noms d’auteurs de 1948 à 2018/19. Paris: Société Mathématique de France (SMF). Astérisque 422, 173-223, Exp. No. 1155 (2020).
MSC:  14F20 14F30
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Hecke operators and systems of eigenvalues on Siegel cusp forms. (English) Zbl 07363184

Memoirs of the American Mathematical Society 1306. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-4334-4/pbk; 978-1-4704-6343-4/ebook). v, 165 p. (2020).
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Proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing a field. (English. Russian original) Zbl 1458.14024

Izv. Math. 84, No. 4, 780-795 (2020); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 84, No. 4, 169-186 (2020).
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Crystalline \(\mathbb{Z}_p\)-representations and \(A_{\inf}\)-representations with Frobenius. (English) Zbl 1440.14118

Bhatt, Bhargav (ed.) et al., \(p\)-adic Hodge theory. Proceedings of the Simons symposium, Schloss Elmau, Germany, May 7–13, 2017. Cham: Springer. Simons Symp., 161-319 (2020).
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Arithmetic Chern-Simons theory. II. (English) Zbl 1440.11207

Bhatt, Bhargav (ed.) et al., \(p\)-adic Hodge theory. Proceedings of the Simons symposium, Schloss Elmau, Germany, May 7–13, 2017. Cham: Springer. Simons Symp., 81-128 (2020).
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On distribution formulas for complex and \(l\)-adic polylogarithms. (English) Zbl 1456.11121

Burgos Gil, José Ignacio (ed.) et al., Periods in quantum field theory and arithmetic. Based on the presentations at the research trimester on multiple zeta values, multiple polylogarithms, and quantum field theory, ICMAT 2014, Madrid, Spain, September 15–19, 2014. Cham: Springer. Springer Proc. Math. Stat. 314, 593-619 (2020).
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Étale monodromy and rational equivalence for 1-cycles on cubic hypersurfaces in \(\mathbb{P}^5\). (English. Russian original) Zbl 1448.14011

Sb. Math. 211, No. 2, 161-200 (2020); translation from Mat. Sb. 211, No. 2, 3-45 (2020).
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