Zobrazeno 1 - 10
of 47
pro vyhledávání: '"Garcia, Elisa Lorenzo"'
Let $C$ be a genus $2$ curve with Jacobian isomorphic to the square of an elliptic curve with complex multiplication by a maximal order in an imaginary quadratic field of discriminant $-d<0$. We show that if the stable model of $C$ has bad reduction
Externí odkaz:
http://arxiv.org/abs/2412.08738
We characterise, in terms of Dixmier-Ohno invariants, the types of singularities that a plane quartic curve can have. We then use these results to obtain new criteria for determining the stable reduction types of non-hyperelliptic curves of genus 3.
Externí odkaz:
http://arxiv.org/abs/2401.13902
In this paper we make explicit the constants of Habegger and Pazuki's work from 2017 on bounding the discriminant of cyclic Galois CM fields corresponding to genus 2 curves with CM by them and potentially good reduction outside a predefined set of pr
Externí odkaz:
http://arxiv.org/abs/2311.13403
In this paper we determine the conductor exponent of non-special Ciani quartics at primes of potentially good reduction in terms of the Ciani invariants. As an intermediate step in order to do so, we provide a reconstruction algorithm to construct Ci
Externí odkaz:
http://arxiv.org/abs/2310.10416
Autor:
van Bommel, Raymond, Docking, Jordan, Dokchitser, Vladimir, Lercier, Reynald, García, Elisa Lorenzo
We give a conjectural characterisation of the stable reduction of plane quartics over local fields in terms of their Cayley octads. This results in p-adic criteria that efficiently give the stable reduction type amongst the 42 possible types, and whe
Externí odkaz:
http://arxiv.org/abs/2309.17381
Which integer sequences are sequences of generalized weights of a linear code? In this paper, we answer this question for linear block codes, rank-metric codes, and more generally for sum-rank metric codes. We do so under an existence assumption for
Externí odkaz:
http://arxiv.org/abs/2307.06595
This paper goes beyond Katz-Sarnak theory on the distribution of curves over finite fields according to their number of rational points, theoretically, experimentally and conjecturally. In particular, we give a formula for the limits of the moments m
Externí odkaz:
http://arxiv.org/abs/2303.17825
Autor:
Ionica, Sorina, Kiliçer, Pinar, Lauter, Kristin, García, Elisa Lorenzo, Mânzăţeanu, Adelina, Vincent, Christelle
In this paper we introduce a new problem called the Isogenous Embedding Problem (IEP). The existence of solutions to this problem is related to the primes of bad reduction of CM curves of genus $3$ and we can detect potentially good reduction in abse
Externí odkaz:
http://arxiv.org/abs/2212.14083
In this paper we inspect from closer the local and global points of the twists of the Klein quartic. For the local ones we use geometric arguments, while for the global ones we strongly use the modular interpretation of the twists. The main result is
Externí odkaz:
http://arxiv.org/abs/2212.10900
For a given genus $g \geq 1$, we give lower bounds for the maximal number of rational points on a smooth projective absolutely irreducible curve of genus $g$ over ${\mathbb F}_q$. As a consequence of Katz-Sarnak theory, we first get for any given $g>
Externí odkaz:
http://arxiv.org/abs/2204.08551