The rank of elliptic surfaces in unramified abelian towers
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| 024 | 7 | 0 | |a 10.1515/crll.2004.2004.577.153 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.1515/crll.2004.2004.577.153 | ||
| 100 | 1 | |a Silverman |D Joseph H. |u 1. Providence. | |
| 245 | 1 | 4 | |a The rank of elliptic surfaces in unramified abelian towers |h [Elektronische Daten] |c [Joseph H. Silverman] |
| 520 | 3 | |a Let ℰ → C be an elliptic surface defined over a number field K. For a finite covering C′ → C defined over K, let ℰ′ = ℰ × C C′ be the corresponding elliptic surface over C′. In this paper we give a strong upper bound for the rank of ℰ′ (C′/K) in the case of geometrically abelian unramified coverings C′ → C and under the assumption that the Tate conjecture is true for ℰ′/K. In the case that C is an elliptic curve and the map C′ = C → C is the multiplication-by-n map, the bound for rank(ℰ′(C′/K)) takes the form O(n k /log log n ), which may be compared with the elementary bound of O(n 2). | |
| 540 | |a © Walter de Gruyter | ||
| 690 | 7 | |a Grammar, syntax, linguistic structure |2 nationallicence | |
| 690 | 7 | |a Phonetics, phonology, prosody |2 nationallicence | |
| 690 | 7 | |a Historical & comparative linguistics |2 nationallicence | |
| 773 | 0 | |t Journal für die reine und angewandte Mathematik (Crelles Journal) |d Walter de Gruyter |g 2004/577(2004-11-30), 153-169 |x 0075-4102 |q 2004:577<153 |1 2004 |2 2004 |o crll | |
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| 908 | |D 1 |a research article |2 jats | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1515/crll.2004.2004.577.153 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Silverman |D Joseph H. |u 1. Providence | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal für die reine und angewandte Mathematik (Crelles Journal) |d Walter de Gruyter |g 2004/577(2004-11-30), 153-169 |x 0075-4102 |q 2004:577<153 |1 2004 |2 2004 |o crll | ||
| 900 | 7 | |b CC0 |u http://creativecommons.org/publicdomain/zero/1.0 |2 nationallicence | |
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