01022nam0 22002531i 450 UON0032820920231205104209.47420090729f |0itac50 baengUS|||| |||||Francisco de los Cobossecretary of the emperor Charles VHayward KenistonPittsburgUniversity of Pittsburg Press, [s. d.]XVI, 463 p.24 cm.CARLO V IMPERATORE DEL SACRO ROMANO IMPERO 1500-1558UONC052695FICOBOS FRANCISCO DE LOSUONC072509FIKENISTONHaywardUONV187004196958University of PittsburghUONV247347650ITSOL20240220RICASIBA - SISTEMA BIBLIOTECARIO DI ATENEOUONSIUON00328209SIBA - SISTEMA BIBLIOTECARIO DI ATENEOSI III STORIAEUR C C 0232 SI MR 70857 5 0232 Francisco de los Cobos1367956UNIOR04897nam 22006013 450 991095533330332120231110212420.097814704723061470472309(CKB)5680000000077045(MiAaPQ)EBC29731919(Au-PeEL)EBL29731919(OCoLC)1343250942(PPN)270358285(EXLCZ)99568000000007704520221021d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierIntrinsic Approach to Galois Theory of 1st ed.Providence :American Mathematical Society,2022.©2022.1 online resource (88 pages)Memoirs of the American Mathematical Society ;v.2799781470453848 1470453843 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. 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.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."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"--Provided by publisher.Memoirs of the American Mathematical Society Galois theoryDifference equationsDifference and functional equations -- Difference equations -- Difference equations, scaling ($q$-differences)mscField theory and polynomials -- Differential and difference algebra -- Difference algebramscGalois theory.Difference equations.Difference and functional equations -- Difference equations -- Difference equations, scaling ($q$-differences).Field theory and polynomials -- Differential and difference algebra -- Difference algebra.515/.625512.3239A1312H10mscVizio Lucia Di1799920Hardouin Charlotte1799921MiAaPQMiAaPQMiAaPQBOOK9910955333303321Intrinsic Approach to Galois Theory of4344351UNINA