Results 21 to 30 of about 36,541 (106)
Rational F-Theory GUTs without exotics [PDF]
, 2014 We construct F-theory GUT models without exotic matter, leading to the MSSM matter spectrum with potential singlet extensions. The interplay of engineering explicit geometric setups, absence of four-dimensional anomalies, and realistic phenomenology of ...
A Font +75 more
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The Frobenius twists of elliptic curves over global function fields
, 2023 25 pages, 0 ...
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On the Mertens Conjecture for Function Fields [PDF]
, 2013 We study an analogue of the Mertens conjecture in the setting of global function fields. Building on the work of Cha, we show that most hyperelliptic curves do not satisfy the Mertens conjecture, but that if we modify the Mertens conjecture to have a ...
Humphries, Peter
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Notes on the Parity Conjecture
, 2012 This is an expository article, based on a lecture course given at CRM Barcelona in December 2009. The purpose of these notes is to prove, in a reasonably self-contained way, that finiteness of the Tate-Shafarevich group implies the parity conjecture for ...
Dokchitser, Tim
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Tetrahedral Elliptic Curves and the local-global principle for Isogenies
, 2014 We study the failure of a local-global principle for the existence of $l$-isogenies for elliptic curves over number fields $K$. Sutherland has shown that over $\mathbb{Q}$ there is just one failure, which occurs for $l=7$ and a unique $j$-invariant, and ...
Banwait, Barinder Singh, Cremona, John
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, 2022 Fix a prime number $p$. Let $\mathbb{F}_q$ be a finite field of characteristic coprime to 2, 3, and $p$, which also contains the primitive $p$-th root of unity $μ_p$. Based on the works by Swinnerton-Dyer and Klagsbrun, Mazur, and Rubin, we prove that the probability distribution of the sizes of prime Selmer groups over a family of cyclic prime twists ...
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Torsion points on elliptic curves over a global field
Manuscripta Mathematica, 1979 Let C be an elliptic curve defined over a global field K and denote by CK the group of rational points of C over K. The classical Nagell-Lutz-Cassels theorem states, in the case of an algebraic number field K as groud field, a necessary condition for a point in CK to be a torsion point, i.e. a point of finite order.
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A heuristic for boundedness of ranks of elliptic curves
, 2018 We present a heuristic that suggests that ranks of elliptic curves over the rationals are bounded. In fact, it suggests that there are only finitely many elliptic curves of rank greater than 21.
Park, Jennifer +3 more
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, 2003 A telegraphic survey of some of the standard results and conjectures about the set $C({\bf Q})$ of rational points on a smooth projective absolutely connected curve $C$ over ${\bf Q}$.Comment: 6 ...
Dalawat, Chandan Singh
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Relations among modular points on elliptic curves
, 2007 Given a correspondence between a modular curve and an elliptic curve A we study the group of relations among the CM points of A. In particular we prove that the intersection of any finite rank subgroup of A with the set of CM points of A is finite.
Buium, Alexandru, Poonen, Bjorn
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