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2-Selmer groups and Heegner points o...
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Li, Chao.
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2-Selmer groups and Heegner points on elliptic curves.
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
2-Selmer groups and Heegner points on elliptic curves./
作者:
Li, Chao.
面頁冊數:
104 p.
附註:
Source: Dissertation Abstracts International, Volume: 77-04(E), Section: B.
Contained By:
Dissertation Abstracts International77-04B(E).
標題:
Mathematics. -
電子資源:
http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3738882
ISBN:
9781339293875
2-Selmer groups and Heegner points on elliptic curves.
Li, Chao.
2-Selmer groups and Heegner points on elliptic curves.
- 104 p.
Source: Dissertation Abstracts International, Volume: 77-04(E), Section: B.
Thesis (Ph.D.)--Harvard University, 2015.
This thesis studies several aspects of the arithmetic of elliptic curves. In particular, we explore the prediction of the Birch and Swinnerton-Dyer conjecture when the 2-Selmer group has rank one.
ISBN: 9781339293875Subjects--Topical Terms:
515831
Mathematics.
2-Selmer groups and Heegner points on elliptic curves.
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104 p.
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Source: Dissertation Abstracts International, Volume: 77-04(E), Section: B.
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Adviser: Benedict Gross.
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Thesis (Ph.D.)--Harvard University, 2015.
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This thesis studies several aspects of the arithmetic of elliptic curves. In particular, we explore the prediction of the Birch and Swinnerton-Dyer conjecture when the 2-Selmer group has rank one.
520
$a
For certain elliptic curves E/Q : y2 = F(x) with additive reduction at 2, we determine their 2-Selmer ranks in terms of the 2-rank of the class group of the cubic field L = Q[x]/F(x). We then interpret this result as a mod 2 congruence between the Hasse-Weil L-function of E and a degree two Artin L-function associated to the cubic field L.
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When the class number of L is odd, the Birch and Swinnerton-Dyer conjecture predicts that E should have rank one over Q(i). To construct such a point on E, we study Heegner points on Shimura curves with non-maximal level at a prime p ramified in the quaternion algebra (in the special case when p = 2). These curves have a p-adic uniformization by a tame etale covering of Drinfeld's p-adic half-plane. We use the covering to describe the geometry of their reduction mod p and compute the Neron model of their Jacobians.
520
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For certain elliptic curves E/Q with good or multiplicative reduction at 2, we study their 2-Selmer groups over imaginary quadratic fields using the method of level raising of modular forms mod p = 2. We prove a parity result (predicted by the Birch and Swinnerton-Dyer conjecture) for 2-Selmer ranks. We also show that there is an obstruction for lowering the 2-Selmer ranks, revealing a different phenomenon compared to odd p.
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http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3738882
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