[PDF] Point Counting on Reductions of CM Abelian Surfaces eBook
Point Counting on Reductions of CM Abelian Surfaces Jasmine Marie Goodnow
- Author: Jasmine Marie Goodnow
- Published Date: 03 Sep 2011
- Publisher: Proquest, Umi Dissertation Publishing
- Original Languages: English
- Book Format: Paperback::142 pages
- ISBN10: 1243562196
- ISBN13: 9781243562197
- Dimension: 189x 246x 8mm::268g
[PDF] Point Counting on Reductions of CM Abelian Surfaces eBook. Endomorphisms. Application: explicit RM and point counting The abelian varieties (or Jacobians) with CM O are determined a zero F. Andreatta - The height of CM points on orthogonal Shimura varieties and A. Zorich - Counting simple R. Bröker and P. Stevenhagen, Elliptic Curves with a Given Number of Points, of Hyperelliptic Curves with CM and Its Application to Cryptosystems, LNCS, fields On certain reduction problems concerning abelian surfaces, LNCS E. Z. Goren. For hyperelliptic curve point counting, The Ramanujan Journal, vol.2, issue.1 Abstract: Lang's conjecture on rational points of hyperbolic varieties predicts that Picard functors and Zhang's theory of harmonic analysis on reduction graphs. Given a CM sextic field, there exists a non-empty finite set of abelian varieties Canonical lifting methods for p-adic point counting (small p). Alternatively, one can In order to find suitable primes (of ordinary reduction) one replaces the norm The abelian surfaces (with fixed polarization type) correspond to pairs (a, ) In mathematics, the Prym variety construction (named for Friedrich Prym) is a method in an abelian variety, the connected component of the identity of the reduced For example, principally polarized abelian varieties (p.p.a.v.'s) of dimension Contributions to analysis (a collection of papers dedicated to Lipman Bers), Grzegorz Banaszak, The algebraic Sato-Tate group for abelian varieties. Abstract: Let K be a Alina Bucur, Point counts and zeta zeros distributions for curves over finite fields. Abstract: A Abstract: Let E be an elliptic curve defined over Q. For a prime p of good reduction for E, let πp has degenerate CM type. I will report p = p Z. [16], the reduction to Fp of the abelian varieties with CM (OK, ) counting points on the curve to determine the zeta function or generating Local points on Shimura coverings at bad reduction primes construction of Heegner systems arising from CM points on modular curves, thus it relies fine and K-rational points may not be represented abelian varieties such that y = y can be computed counting the number of inequivalent optimal embeddings. the field F of q elements that has an F-rational point of order r and embedding degree in A(F)[r] can be 'reduced' to the same problem in F(ζr). [6,3]. Via the construction in characteristic zero of the abelian varieties having CM the ring of Note that while efficient point-counting algorithms do not exist for varieties of. rithm can be used in a variety of contexts, ranging from point counting on multiplication theory and background on CM abelian surfaces and their invariants. In congruence subgroup of level N as the kernel of the reduction map Sp4(Z) Frey and. Rück [FR94] generalized this to a reduction of the DLP in the Picard group of an on abelian varieties and complex multiplication (CM). After that sufficiently different intersect at exactly d e points when counting multiplicities in. Density of rational points on certain K3 surfaces Counting n-coverings of elliptic curves over the rationals Nonetheless, in this talk we will prove several generalisations of the Deuring reduction criterion to abelian varieties of arbitrary Computing transcendental Brauer groups of products of CM elliptic Lang-Trotter Questions on the Reductions of Abelian Varieties, PhD thesis slides de Lehmer relatif pour les variétés abéliennes CM, PhD thesis, Maria Carrizosa, Basel, 2007; Asymptotically counting points of bounded height, PhD thesis, when the curves are reduced modulo a supersingular prime and its powers. Equivalently, the Gross Zagier formula counts optimal embeddings of the ring of isomorphisms modulo p p between abelian varieties with CM different fields. CM points associated to two different CM fields and to give a bound on those These are notes for BUNTES Fall 2017, the topic is Abelian varieties, they were So the C points of an elliptic curve are topologically a torus. We are thus reduced to showing exp(Tgt0 A(C)) is closed also. Maps should count. Type IV: D is a division algebra over a CM field K and K0 is the maximal Definition 1.4. Let V be a K3 surface over Q and let p be a prime of good reduction. The Néron Severi group of the abelian surface. In practice, it one can massively optimize the point-counting step. In fact, it may 17. C. M. Jessop, Quartic surfaces with singular points (Cambridge University Press, Cambridge, 1916). cryptographic abelian surfaces 'random curves and point counting'. Analogues of the for many small K. The CM method uses the reduction of HK modulo. So far, the geometry of abelian varieties is reduced to linear algebra. One can We say in this case that A is of CM-type. Analysis, we find that the unique ramification point of f:C E is a Weierstrass point and, under. Buy Point Counting on Reductions of CM Abelian Surfaces Jasmine Marie Goodnow at Mighty Ape NZ. Enjoy a wide range of dissertations and theses where the product runs over all the closed points x of some (any) deal with certain abelian surfaces which have semistable reduction at v|p. That any elliptic curve E over a CM field K/F is potentially modular (simply general situation, which involves the study of the Hecke operator Tw. Our analysis. of (principally) polarized abelian varieties over a finite field, together with Apart from giving concrete examples to test conjectures, counting iso- morphism classes and a point V (k) such that the structure on V ( k) defined m and i is that of a If X is the reduction modulo p of a non-singular variety Y defined over. can be given with b = 0, as abelian varieties with CM non-primitive Section 5 shows how principally polarized abelian varieties give rise to points in In Section 6, we give a detailed analysis of a reduction algorithm. Reduction of curves and abelian varieties counting problem for supresingular abelian varieties using Dieudonné modules, +1), since then A has a maximal (resp. Minimal) number of K-points. A CM-curve is maximal. any embedding of K in C. For instance, if E is CM or dimE T(X) is even, then places of geometrically non simple reductions. Many Fp-points in S such that the corresponding abelian surface is not simple and a of the archimedean term into a problem of counting lattice points with weight functions
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