Academic literature on the topic 'Poitou-Tate duality'
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Journal articles on the topic "Poitou-Tate duality":
Geisser, Thomas H., and Alexander Schmidt. "Poitou–Tate duality for arithmetic schemes." Compositio Mathematica 154, no. 9 (August 23, 2018): 2020–44. http://dx.doi.org/10.1112/s0010437x18007340.
Lim, Meng Fai. "Poitou–Tate duality over extensions of global fields." Journal of Number Theory 132, no. 11 (November 2012): 2636–72. http://dx.doi.org/10.1016/j.jnt.2012.05.007.
Blumberg, Andrew J., and Michael A. Mandell. "K-theoretic Tate–Poitou duality and the fiber of the cyclotomic trace." Inventiones mathematicae 221, no. 2 (February 4, 2020): 397–419. http://dx.doi.org/10.1007/s00222-020-00952-z.
Rosengarten, Zev. "Tate Duality In Positive Dimension over Function Fields." Memoirs of the American Mathematical Society 290, no. 1444 (October 2023). http://dx.doi.org/10.1090/memo/1444.
Asensouyis, Hassan, Jilali Assim, Zouhair Boughadi, and Youness Mazigh. "Poitou–Tate duality for totally positive Galois cohomology." Communications in Algebra, April 25, 2022, 1–22. http://dx.doi.org/10.1080/00927872.2022.2060995.
Dissertations / Theses on the topic "Poitou-Tate duality":
Nguyen, Manh-Linh. "Cohomological studies of rational points over fields of arithmetico-geometric nature." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM010.
In this thesis, we study various arithmetic problems, notably the existence of rational points and weak approximation on certain varieties over number fields and their geometric analogues.After the first introductory chapter, we present in the second one some results obtained by computations with (abelian or nonabelian) Galois cocycles. First, we consider a formula of Borovoi-Demarche-Harari for the unramified algebraic Brauer group of homogeneous spaces. Then, we establish the Hasse principle and weak approximation for a class of homogeneous spaces of SLn over number fields, whose geometric stabilizers are finite of nilpotency class 2, constructed by Borovoi and Kunyavskii. This is a small step towards a conjecture of Colliot-Thélène on the Brauer-Manin obstruction for rationally connected varieties.The third chapter is devoted to a recently formulated conjecture by Wittenberg, which concerns descent theory (a method orginially developped by Colliot-Thélène and Sansuc). We prove this conjecture for torsors under a connected linear algebraic group, generalizing a previous result of Harpaz and Wittenberg for torsors under a torus. We do this by adapting their technique with Borovoi's machinery of abelianization of non-abelian Galois cohomology. We shall also prove a version of this “descent conjecture” in the context of zero-cycles.In this last chapter, we follow the works of Harari-Scheiderer-Szamuely, Izquierdo and Tian, by studying the local-global principle and weak approximation over p-adic function fields. Over these fields, which are fields of cohomological dimension 3, there exists a higher-dimensional analogue of the Brauer-Manin obstruction that relies on the generalized Weil reciprocity law. Here, we apply Poitou-Tate style duality theorems to obtain some results for certain homogeneous spaces. We also consider some function fields of cohomological dimension greater than 3
Book chapters on the topic "Poitou-Tate duality":
Harari, David. "Poitou–Tate Duality." In Galois Cohomology and Class Field Theory, 259–78. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43901-9_17.
Stix, Jakob. "Fragments of Non-abelian Tate–Poitou Duality." In Lecture Notes in Mathematics, 147–54. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-30674-7_12.
"CHAPITRE 17 DUALITÉ DE POITOU-TATE." In Cohomologie galoisienne, 277–98. EDP Sciences, 2020. http://dx.doi.org/10.1051/978-2-7598-2067-2-019.
"CHAPITRE 17 DUALITÉ DE POITOU-TATE." In Cohomologie galoisienne, 277–98. EDP Sciences, 2020. http://dx.doi.org/10.1051/978-2-7598-2067-2.c019.