On Selmer groups of abelian varieties over ℓ\ell-adic Lie extensions of global function fields

Let $F$ be a global function field of characteristic $p>0$ and $A/F$ an abelian variety. Let $K/F$ be an \l-adic Lie extension (\l\neq p) unramified outside a finite set of primes $S$ and such that \Gal(K/F) has no elements of order \l. We shall prove that, under certain conditions, Sel_A(K)_\l^\vee has no nontrivial pseudo-null submodule.Comment: 14 page

Euler characteristic and Akashi series for Selmer groups over global function fields

Let $A$ be an abelian variety defined over a global function field $F$ of positive characteristic $p$ and let $K/F$ be a $p$-adic Lie extension with Galois group $G$. We provide a formula for the Euler characteristic $\chi(G,Sel_A(K)_p)$ of the $p$-part of the Selmer group of $A$ over $K$. In the special case $G=\mathbb{Z}_p^d$ and $A$ a constant ordinary variety, using Akashi series, we show how the Euler characteristic of the dual of $Sel_A(K)_p$ is related to special values of a $p$-adic $\mathcal{L}$-function

In vitro evaluation of an air-abrasion cavity preparation system (KCP 2000) for bonded restorations

Thesis (M.Sc.D.)--Boston University, Henry M. Goldman School of Graduate Dentistry, 1995 (Pediatric Dentistry).Includes bibliographical references (leaves 97-101).This study tested a new air-abrasive system (KCP 2000, American Dental Technologies, Troy, MI) as a substitute for acid etching to condition enamel and dentin surfaces for sealants and bonded composite restorations. Thirty specimens were tested for shear bond strength of composite to enamel surface conditioned with: 1) 10% maleic acid, 15 sec. (control); 2) air-abrasion at 120 psi and 50 [mu]m particle size, 3 sec.; and 3) air-abrasion plus maleic acid. Thirty specimens were tested for composite shear bond strength to dentin conditioned with: 4) 10% maleic acid, 15 sec. (control); 5) air-abrasion at 120 psi and 50 [mu]m particle size, 3 sec.; and 6) air-abrasion plus maleic acid. Thirty specimens were tested for shear bond strength of sealant to enamel surface conditioned with: 7) 37% orthophosphoric acid, 60 sec. (control); 8) air-abrasion at 120 psi and 50[mu]m particle size, 3 sec.; and 9) air-abrasion plus orthophosphoric acid. Marginal microleakage of twelve molars with a class V composite restoration prepared with a 330 high speed bur and conditioned with 10% maleic acid was compared to eleven molars with a class V composite restoration prepared with air-brasion at 160 psi and 27 [mu]m particles size and conditioned at 120 psi and 50 [mu]m particle size. All the samples from microleakage and shear bond strength tests were thermocycled for 300 cycles between 5[degrees]C and 60[degrees]C[plus or minus]2[degrees] with a dwell time of 30 sec. and transfer time of 15 sec. The shear bond strength results were recorded in MPa and were as follows: Composite to enamel, group 1: 10.7[plus or minus]3.6, group 2: all specimens failed before the shear bond strength test, group 3: 14[plus or minus]1.9; Composite to dentin, group 4: 18.5[plus or minus]5.1, group 5: 3.1[plus or minus]2.0, group 6: 11.1[plus or minus]5.8; Sealant to enamel, group 7: 7.5[plus or minus]2.0, group 8: 0.3[plus or minus]0.1, group 9: 9.7[plus or minus]3. The ANOVA test and Scheffe Pairwise Comparisons tests for the composite to dentin group showed that the acid etching was significantly stronger than the air-abrasion treatment alone, but equivalent to the air-abrasi6n plus the acid etching (p[less than or equal to]0.01). The student t-test applied to the sealant to enamel group revealed that bond strength with acid etching was significantly higher than air-abrasion (p[less than]0.001). The mean marginal microleakage values (mm) were as follows: Air-abrasion group, occlusal site: 0.75[plus or minus]0.2, cervical site: 0.7[plus or minus]0.4; 330 bur group, occlusal site: 0.46[plus or minus]0.2, cervical site: 0.86[plus or minus]0.4. The ANOVA and Scheffe Pairwise Comparisons tests showed a significantly higher microleakage in the cervical site of the 330 bur group (p[less than or equal to]0.01). This study showed that the air-abrasive technique can be effective for bonding when used in conjunction with acid etching but it cannot be used as a sole conditioner prior to bonding composite or sealant to enamel or dentin

Control theorems for l-adic Lie extensions of global function fields

Let F be a global function field of characteristic p>0, K/F an l-adic Lie extension unramified outside a finite set of places S and A/F an abelian variety. We study Sel_A(K)_l^ee (the Pontrjagin dual of the Selmer group) and (under some mild hypotheses) prove that it is a finitely generated Z_l[[Gal(K/F)]]-module via generalizations of Mazur's Control Theorem. If Gal(K/F) has no elements of order l and contains a closed normal subgroup H such that Gal(K/F)/H simeq Z_l, we are able to give sufficient conditions for Sel_A(K)_l^ee to be finitely generated as Z_l[[H]]-module and, consequently, a torsion Z_l[[Gal(K/F)]]-module. We deal with both cases l eq p and l=p