297 research outputs found
On central leaves of Hodge-type Shimura varieties with parahoric level structure
Kisin and Pappas constructed integral models of Hodge-type Shimura varieties
with parahoric level structure at , such that the formal neighbourhood of
a mod~ point can be interpreted as a deformation space of -divisible
group with some Tate cycles (generalising Faltings' construction). In this
paper, we study the central leaf and the closed Newton stratum in the formal
neighbourhoods of mod~ points of Kisin-Pappas integral models with parahoric
level structure; namely, we obtain the dimension of central leaves and the
almost product structure of Newton strata. In the case of hyperspecial level
strucure (i.e., in the good reduction case), our main results were already
obtained by Hamacher, and the result of this paper holds for ramified groups as
well.Comment: 33 pages; section 2.5 added to fill in the gap in the earlier versio
On the structure of signed Selmer groups
Let be a number field unramified at an odd prime and be the -cyclotomic extension of . Generalizing Kobayashi plus/minus Selmer groups for elliptic curves, B\"uy\"ukboduk and Lei have defined modified Selmer groups, called signed Selmer groups, for certain non-ordinary -representations. In particular, their construction applies to abelian varieties defined over with good supersingular reduction at primes of dividing . Assuming that these Selmer groups are cotorsion -modules, we show that they have no proper sub--module of finite index. We deduce from this a number of arithmetic applications. On studying the Euler-Poincar\'e characteristic of these Selmer groups, we obtain an explicit formula on the size of the Bloch-Kato Selmer group attached to these representations. Furthermore, for two such representations that are isomorphic modulo , we compare the Iwasawa-invariants of their signed Selmer groups
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