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Lie invariant Frobenius lifts.
- Source :
-
Journal of Number Theory . Jun2024, Vol. 259, p378-418. 41p. - Publication Year :
- 2024
-
Abstract
- We begin with the observation that the p -adic completion of any affine elliptic curve with ordinary reduction possesses Frobenius lifts ϕ that are "Lie invariant mod p " in the sense that the "normalized" action of ϕ on 1-forms preserves mod p the space of invariant 1-forms. Our main result is that, after removing the 2-torsion sections, the above situation can be "infinitesimally deformed" in the sense that the above mod p result has a mod p 2 analogue. We end by showing that, in contrast with the case of elliptic curves, the following holds: if G is a linear algebraic group over a number field and if G is not a torus then for all but finitely many primes p the p -adic completion of G does not possess a Frobenius lift that is Lie invariant mod p. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ELLIPTIC curves
*DIFFERENTIAL forms
*LINEAR algebraic groups
*MODULAR forms
Subjects
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 259
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 175849576
- Full Text :
- https://doi.org/10.1016/j.jnt.2024.01.019