{"text_format":"2","workbook":"xls","n_sheets":1,"sheets":["report2"],"not_rendered":{"charts":0,"images":0,"macros":0,"external_links":1,"defined_names":1,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"run_cost":"one","rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"report2","index":0,"n_rows":24,"n_cols":5,"rows_kept":24,"cut":false,"hidden":false,"merged":[[0,2,0,3],[0,4,0,5],[1,2,1,3],[1,4,1,5],[2,2,2,3],[2,4,2,5],[3,2,3,3],[5,2,5,3],[7,2,7,3],[8,2,8,3],[9,2,9,3],[10,2,10,3],[11,2,11,3],[13,2,13,3],[17,2,17,3],[18,2,18,3],[20,2,20,3]],"flags":["formulas_cached_only"]}
[null,"1.","Record Nr.",null,"UNINA9910955333303321"]
[null,null,"Autore",null,"Vizio Lucia Di"]
[null,null,"Titolo",null,"Intrinsic Approach to Galois Theory of"]
[null,null,"Pubbl/distr/stampa",null,"Providence : , : American Mathematical Society, , 2022"]
[{"$nulls":4},"©2022"]
[null,null,"ISBN",null,"9781470472306"]
[{"$nulls":4},"1470472309"]
[null,null,"Edizione",null,"[1st ed.]"]
[null,null,"Descrizione fisica",null,"1 online resource (88 pages)"]
[null,null,"Collana",null,"Memoirs of the American Mathematical Society ; ; v.279"]
[null,null,"Classificazione",null,"39A1312H10"]
[null,null,"Disciplina",null,"515/.625"]
[{"$nulls":4},"512.32"]
[null,null,"Soggetti",null,"Galois theory"]
[{"$nulls":4},"Difference equations"]
[{"$nulls":4},"Difference and functional equations -- Difference equations -- Difference equations, scaling ($q$-differences)"]
[{"$nulls":4},"Field theory and polynomials -- Differential and difference algebra -- Difference algebra"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,"Nota di contenuto",null,"Cover -- Title page -- Introduction -- Grothendieck conjecture for  -difference equations -- Intrinsic Galois groups -- Comparison with Malgrange-Granier Galois theory for non-linear differential equations -- Acknowledgments -- Part 1. Introduction to  -difference equations -- Chapter 1. Generalities on  -difference modules -- 1.1. Basic definitions -- 1.2.  -difference modules, systems and equations -- 1.3. Some remarks on solutions -- 1.4. Trivial  -difference modules -- Chapter 2. Formal classification of singularities -- 2.1. Regularity -- 2.2. Irregularity -- Part 2. Triviality of  -difference equations with rational coefficients -- Chapter 3. Rationality of solutions, when   is an algebraic number -- 3.1. The case of   algebraic, not a root of unity -- 3.2. Global nilpotence. -- 3.3. Proof of Theorem 3.8 (and of Theorem 3.6) -- Chapter 4. Rationality of solutions when   is transcendental -- 4.1. Statement of the main result -- 4.2. Regularity and triviality of the exponents -- 4.3. Proof of Theorem 4.2 -- 4.4. Link with iterative  -difference equations -- Chapter 5. A unified statement -- Part 3. Intrinsic Galois groups -- Chapter 6. The intrinsic Galois group -- 6.1. Definition and first properties -- 6.2. Arithmetic characterization of the intrinsic Galois group -- 6.3. Finite intrinsic Galois groups -- 6.4. "]
[{"$nulls":4},"Intrinsic Galois group of a  -difference module over \\C( ), for  ̸=0,1 -- Chapter 7. The parametrized intrinsic Galois group -- 7.1. Differential and difference algebra -- 7.2. Parametrized intrinsic Galois groups -- 7.3. Characterization of the parametrized intrinsic Galois group by curvatures -- 7.4. Parametrized intrinsic Galois group of a  -difference module over \\C( ), for  ̸=0,1 -- 7.5. The example of the Jacobi Theta function -- Part 4. Comparison with the non-linear theory."]
[{"$nulls":4},"Chapter 8. Preface to Part 4. The Galois  -groupoid of a  -difference system, by Anne Granier -- 8.1. Definitions -- 8.2. A bound for the Galois  -groupoid of a linear  -difference system -- 8.3. Groups from the Galois  -groupoid of a linear  -difference system -- Chapter 9. Comparison of the parametrized intrinsic Galois group with the Galois  -groupoid -- 9.1. The Kolchin closure of the Dynamics and the Malgrange-Granier groupoid -- 9.2. The groupoid \\Gal{ ( )} -- 9.3. The Galois  -groupoid \\Galan{ ( )} vs the intrinsic parametrized Galois group -- 9.4. Comparison with known results -- Bibliography -- Back Cover."]
[null,null,null,"Sommario/riassunto","\"The Galois theory of difference equations has witnessed a major evolution in the last two decades. In the particular case of q-difference equations, authors have introduced several different Galois theories. In this memoir we consider an arithmetic approach to the Galois theory of q-difference equations and we use it to establish an arithmetical description of some of the Galois groups attached to q-difference systems\"--"]