# Frobenius modules and Galois representations

B. Heinrich Matzat^{[1]}

- [1] University of Heidelberg Interdisciplinary Center for Scientific Computing Im Neuheimer Feld 368 69120 Heidelberg (Germany)

Annales de l’institut Fourier (2009)

- Volume: 59, Issue: 7, page 2805-2818
- ISSN: 0373-0956

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topMatzat, B. Heinrich. "Frobenius modules and Galois representations." Annales de l’institut Fourier 59.7 (2009): 2805-2818. <http://eudml.org/doc/10472>.

@article{Matzat2009,

abstract = {Frobenius modules are difference modules with respect to a Frobenius operator. Here we show that over non-archimedean complete differential fields Frobenius modules define differential modules with the same Picard-Vessiot ring and the same Galois group schemes up to extension by constants. Moreover, these Frobenius modules are classified by unramified Galois representations over the base field. This leads among others to the solution of the inverse differential Galois problem for $p$-adic differential equations with (strong) Frobenius structure over $p$-adic differential fields with algebraically closed residue field.},

affiliation = {University of Heidelberg Interdisciplinary Center for Scientific Computing Im Neuheimer Feld 368 69120 Heidelberg (Germany)},

author = {Matzat, B. Heinrich},

journal = {Annales de l’institut Fourier},

keywords = {Frobenius modules; iterative differential modules; Galois representations; $p$-adic differential equations; inverse differential Galois theory; -adic differential equations},

language = {eng},

number = {7},

pages = {2805-2818},

publisher = {Association des Annales de l’institut Fourier},

title = {Frobenius modules and Galois representations},

url = {http://eudml.org/doc/10472},

volume = {59},

year = {2009},

}

TY - JOUR

AU - Matzat, B. Heinrich

TI - Frobenius modules and Galois representations

JO - Annales de l’institut Fourier

PY - 2009

PB - Association des Annales de l’institut Fourier

VL - 59

IS - 7

SP - 2805

EP - 2818

AB - Frobenius modules are difference modules with respect to a Frobenius operator. Here we show that over non-archimedean complete differential fields Frobenius modules define differential modules with the same Picard-Vessiot ring and the same Galois group schemes up to extension by constants. Moreover, these Frobenius modules are classified by unramified Galois representations over the base field. This leads among others to the solution of the inverse differential Galois problem for $p$-adic differential equations with (strong) Frobenius structure over $p$-adic differential fields with algebraically closed residue field.

LA - eng

KW - Frobenius modules; iterative differential modules; Galois representations; $p$-adic differential equations; inverse differential Galois theory; -adic differential equations

UR - http://eudml.org/doc/10472

ER -

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