Lai, KF and Longhi, I and Suzuki, T and Tan, KS and Trihan, F (2021) On the Âµinvariants of abelian varieties over function fields of positive characteristic. In: Algebra and Number Theory, 15 (4). pp. 863907.

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Abstract
Let A be an abelian variety over a global function field K of characteristic p. We study the Âµinvariant appearing in the Iwasawa theory of A over the unramified â�¤pextension of K. Ulmer suggests that this invariant is equal to what he calls the dimension of the Tateâ��Shafarevich group of A and that it is indeed the dimension of some canonically defined group scheme. Our first result is to verify his suggestions. He also gives a formula for the dimension of the Tateâ��Shafarevich group (which is now the Âµinvariant) in terms of other quantities including the Faltings height of A and Frobenius slopes of the numerator of the Hasseâ��Weil Lfunction of A/K assuming the conjectural Birchâ��SwinnertonDyer formula. Our next result is to prove this Âµinvariant formula unconditionally for Jacobians and for semistable abelian varieties. Finally, we show that the â��Âµ = 0â�� locus of the moduli of isomorphism classes of minimal elliptic surfaces endowed with a section and with fixed large enough Euler characteristic is a dense open subset. Â© 2021 Mathematical Sciences Publishers.
Item Type:  Journal Article 

Publication:  Algebra and Number Theory 
Publisher:  Mathematical Science Publishers 
Additional Information:  The copyright for this article belongs to Authors 
Department/Centre:  Division of Physical & Mathematical Sciences > Mathematics 
Date Deposited:  06 Aug 2021 08:17 
Last Modified:  06 Aug 2021 08:17 
URI:  http://eprints.iisc.ac.in/id/eprint/69037 
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