The splitting fields and Generators of Shioda's elliptic surfaces $y^2=x^3 +t^{m} +1$ (I)

Fuente: arXiv

Salvato in:

Dettagli Bibliografici
Autori principali:	Salami, Sajad, Zargar, Arman Shamsi
Natura:	Preprint
Pubblicazione:	2025
Soggetti:	Number Theory Algebraic Geometry 14J27, 11G05
Accesso online:	Acceder al recurso
Tags:	Aggiungi Tag Nessun Tag, puoi essere il primo ad aggiungerne!!

Documenti analoghi

Generators and splitting fields of certain elliptic K3 surfaces
di: Salami, Sajad, et al.
Pubblicazione: (2022)

Counting rational points on elliptic and hyperelliptic curves over function fields
di: Gillibert, Jean, et al.
Pubblicazione: (2025)

The splitting field and generators of the elliptic surface $Y^2=X^3 +t^{360} +1$
di: Salami, Sajad
Pubblicazione: (2025)

Conic bundles and Mordell--Weil ranks of elliptic surfaces
di: Meira, Felipe Zingali
Pubblicazione: (2024)

A note on a question of Shioda about integral sections
di: Mo, Jia-Li
Pubblicazione: (2024)

Non-thin rational points for elliptic K3 surfaces
di: Gvirtz-Chen, Damián, et al.
Pubblicazione: (2024)

Integral points on elliptic curves with $j$-invariant $0$ over $k(t)$
di: Gillibert, Jean, et al.
Pubblicazione: (2023)

On Properly $θ$-Congruent Numbers Over Real Number Fields
di: Salami, Sajad, et al.
Pubblicazione: (2025)

Higher modularity of elliptic curves over function fields
di: Logan, Adam, et al.
Pubblicazione: (2022)

Iwasawa Main Conjecture for ordinary semistable elliptic curves over global function fields
di: Tan, Ki-Seng, et al.
Pubblicazione: (2026)

Vojta's conjecture on weighted projective varieties
di: Salami, Sajad, et al.
Pubblicazione: (2023)

Hilbert property for low-genus families and degree-one del Pezzo surfaces
di: Demeio, Julian, et al.
Pubblicazione: (2025)

Prime order torsion on elliptic curves over number fields. Part I: Asymptotics
di: Derickx, Maarten, et al.
Pubblicazione: (2025)

Five-dimensional compatible systems and the Tate conjecture for elliptic surfaces
di: Duan, Lian, et al.
Pubblicazione: (2024)

Rank jumps and Multisections of elliptic fibrations on K3 surfaces
di: Garbagnati, Alice, et al.
Pubblicazione: (2025)

Rank of Jacobian Varieties of Curves $y^s=x(ax^r+b)$
di: Salami, Sajad
Pubblicazione: (2025)

The $μ$-invariant change for abelian varieties over finite $p$-extensions of global fields
di: Tan, Ki-Seng, et al.
Pubblicazione: (2023)

Iitaka fibrations and integral points: a family of arbitrarily polarized spherical threefolds
di: Derenthal, Ulrich, et al.
Pubblicazione: (2025)

The Mahler measure of exact polynomials and special $L$-values of $K3$ surfaces
di: Trieu, Thu Ha
Pubblicazione: (2024)

Isogenies between $K3$ surfaces of the Apéry-Fermi pencil
di: Bertin, Marie José, et al.
Pubblicazione: (2022)

Rational curves and the Hilbert Property on Jacobian Kummer varieties
di: Gvirtz-Chen, Damián, et al.
Pubblicazione: (2022)

Integral Diophantine approximation on varieties
di: Huang, Zhizhong, et al.
Pubblicazione: (2025)

Rational distances from given rational points in the plane
di: Corvaja, Pietro, et al.
Pubblicazione: (2024)

On the infinitude of elliptic curves over a number field with prescribed small rank
di: Zywina, David
Pubblicazione: (2026)

Moderate rank jumps on rational elliptic surfaces via construction of conics
di: Desjardins, Julie
Pubblicazione: (2025)

Transcendental Brauer-Manin obstructions on singular K3 surfaces
di: Tawfik, Mohamed Alaa, et al.
Pubblicazione: (2023)

Desingularization of double covers of regular surfaces
di: Liu, Qing
Pubblicazione: (2025)

Galois Realisations of $\operatorname{PSL}_2(\mathbb{F}_{p^2})$ via non-unirational Hilbert Irreducibility
di: Demeio, Julian, et al.
Pubblicazione: (2025)

Sesquilinear pairings on elliptic curves
di: Stange, Katherine E.
Pubblicazione: (2024)

Kato-Kuzumaki's properties for function fields over higher local fields
di: Gambardella, Felipe
Pubblicazione: (2025)

Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields
di: Shankar, Ananth N., et al.
Pubblicazione: (2019)

Stability of the Kato-Kuzumaki's properties under field extensions
di: Gambardella, Felipe, et al.
Pubblicazione: (2025)

The intrinsic subgroup of an elliptic curve and Mazur's torsion theorem
di: Yamazaki, Takao, et al.
Pubblicazione: (2025)

Weak weak approximation and the Hilbert property for degree-two del Pezzo surfaces
di: Demeio, Julian Lawrence, et al.
Pubblicazione: (2023)

On Kato and Kuzumaki's properties for the Milnor $K_2$ of function fields of $p$-adic curves
di: Izquierdo, Diego, et al.
Pubblicazione: (2022)

del Pezzo surfaces with one bad prime over cyclotomic $\mathbb{Z}_\ell$-extensions
di: Nowroozi, Maryam
Pubblicazione: (2025)

The Picard group of the Baily--Borel compactification of the moduli space of quasi-polarized K3 surfaces and generalizations
di: Huang, Chenxin, et al.
Pubblicazione: (2024)

Isogeny relations in products of families of elliptic curves
di: Ferrigno, Luca
Pubblicazione: (2024)

A geometric determinant method and geometric dimension growth
di: Buggenhout, Tijs, et al.
Pubblicazione: (2025)

Integral points on singular del Pezzo surfaces
di: Derenthal, Ulrich, et al.
Pubblicazione: (2021)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
language	"it"
ui	"standard"
VUFIND_SESSION	"5e8a09298d03c1ce5b24404de5514253"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1791214096.4694 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "5e8a09298d03c1ce5b24404de5514253" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"language=it; ui=standard; VUFIND_SESSION=5e8a09298d03c1ce5b24404de5514253"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.217.58"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"25698"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2512_16578/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2512_16578/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1791214096.4646
REQUEST_TIME	1791214096

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler