On Some Questions Related to the Krichever Correspondence
Matematičeskie zametki, Tome 81 (2007) no. 4, pp. 528-539.

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We investigate various new properties and examples of the two-dimensional and one-dimensional Krichever correspondence.
Keywords: algebraic curve, torsion-free sheaf, cohomology group, Krichever correspondence, Fredholm subspace.
Mots-clés : ample Cartier divisor
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A. B. Zheglov; D. V. Osipov. On Some Questions Related to the Krichever Correspondence. Matematičeskie zametki, Tome 81 (2007) no. 4, pp. 528-539. http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a5/

[1] M. Mulase, “Solvability of the super KP equation and a generalization of the Birkhoff decomposition”, Invent. Math., 92:1 (1988), 1–46 | DOI | MR | Zbl

[2] A. N. Parshin, “O koltse formalnykh psevdodifferentsialnykh operatorov”, Tr. MIAN, 224:1 (1999), 291–305 ; arXiv:math.AG/9911098 | MR | Zbl

[3] A. B. Zheglov, “O strukture dvumernykh lokalnykh tel”, Izv. RAN. Ser. matem., 65:1 (2001), 25–60 | MR | Zbl

[4] M. Mulase, “Category of vector bundles on algebraic curves and infinite dimensional Grassmannians”, Int. J. Math., 1:3 (1990), 293–342 | DOI | MR | Zbl

[5] G. Sigal, Dzh. Vilson, “Gruppy petel i uravneniya tipa KdF”, dopolnenie k knige E. Pressli, G. Sigal, Gruppy petel, Mir, M., 1990, 379–442 | MR | Zbl

[6] D. V. Osipov, “Beskonechnomernyi grassmanian Sato i kogerentnye puchki ranga $2$ na krivykh”, Matem. sb., 194:11 (2003), 81–94 | MR | Zbl

[7] A. N. Parshin, “Sootvetstvie Krichevera dlya algebraicheskikh poverkhnostei”, Funktsion. analiz i ego prilozh., 35:1 (2001), 88–90 ; arXiv:math.AG/9911097 | MR | Zbl

[8] A. N. Parshin, “Integrable systems and local fields”, Comm. Algebra, 29:9 (2001), 4157–4181 | DOI | MR | Zbl

[9] A. N. Parshin, “K arifmetike dvumernykh skhem. I. Raspredeleniya i vychety”, Izv. AN SSSR. Ser. Matem., 40:4 (1976), 736–773 | MR | Zbl

[10] T. Fimmel, A. N. Parshin, An Introduction to the Higher Adelic Theory, preprint

[11] A. Huber, “On the Parshin–Beilinson adeles for schemes”, Abh. Math. Sem. Univ. Hamburg, 61 (1991), 249–273 | DOI | MR | Zbl

[12] D. V. Osipov, “$n$-dimensional local fields and adeles on $n$-dimensional schemes”, Lecture Notes Series of London Math. Soc. (to appear)

[13] D. V. Osipov, “Sootvetstvie Krichevera dlya algebraicheskikh mnogoobrazii”, Izv. RAN. Ser. matem., 65:5 (2001), 91–128 ; arXiv:math.AG/0003188 | MR | Zbl

[14] M. Noumi, Notes to the book by M. Sato, Soliton equations and universal Grassmann manifold, Sophia Kokyuroku in Mathematics, 18, Sophia University, Tokyo, 1984, 74–75 | Zbl

[15] M. Sato, Y. Sato, “Soliton equations as dynamical systems on infinite dimensional Grassmann manifold”, Nonlinear partial differential equations in applied science (Tokyo, 1982), North-Holland Math. Stud., 81, North-Holland, Amsterdam, 1983, 259–271 | MR | Zbl

[16] A. B. Zheglov, Two dimensional KP systems and their solvability, arXiv:math-ph/0503067