Arithmetic theory of q-difference equations. The q-analogue of Grothendieck-Katz's conjecture on p-curvatures
Di Vizio, Lucia
HAL, hal-00021535 / Harvested from HAL
Text on HAL
Grothendieck's conjecture on p-curvatures predicts that an arithmetic differential equation has a full set of algebraic solutions if and only if its reduction in positive characteristic has a full set of rational solutions for almost all finite places. It is equivalent to Katz's conjectural description of the generic Galois group. In this paper we prove an analogous statement for arithmetic q-difference equation.
Publié le : 2002-07-05
Classification:  [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT],  [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA] 
@article{hal-00021535,
     author = {Di Vizio, Lucia},
     title = {Arithmetic theory of q-difference equations. The q-analogue of Grothendieck-Katz's conjecture on p-curvatures},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00021535}
}

Di Vizio, Lucia. Arithmetic theory of q-difference equations. The q-analogue of Grothendieck-Katz's conjecture on p-curvatures. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00021535/