The rigid analytical regulator and K_2 of Drinfeld modular curves

We evaluate a rigid analytical analogue of the Beilinson-Bloch-Deligne regulator on certain explicit elements in the K_2 of Drinfeld modular curves, constructed from analogues of modular units, and relate its value to special values of L-series using the Rankin-Selberg method.Comment: 38 pages, to appear in Publ. Res. Inst. Math. Sc

On the kernel and the image of the rigid analytic regulator in positive characteristic

We will formulate and prove a certain reciprocity law relating certain residues of the differential symbol dlog^2 from the K_2 of a Mumford curve to the rigid analytic regulator constructed by the author in a previous paper. We will use this result to deduce some consequences on the kernel and image of the rigid analytic regulator analogous to some old conjectures of Beilinson and Bloch on the complex analytic regulator. We also relate our construction to the symbol defined by Contou-Carrere and to Kato's residue homomorphism, and we show that Weil's reciprocity law directly implies the reciprocity law of Anderson and Romo.Comment: 28 pages, to appear in Publ. Res. Inst. Math. Sc

The pp-adic monodromy group of abelian varieties over global function fields of characteristic pp

We prove an analogue of the Tate isogeny conjecture and the semi-simplicity conjecture for overconvergent crystalline Dieudonn\'e modules of abelian varieties defined over global function fields of characteristic $p$. As a corollary we deduce that monodromy groups of such overconvergent crystalline Dieudonn\'e modules are reductive, and after a finite base change of coefficients their connected components are the same as the connected components of monodromy groups of Galois representations on the corresponding $l$-adic Tate modules, for $l$ different from $p$. We also show such a result for general compatible systems incorporating overconvergent $F$-isocrystals, conditional on a result of Abe.Comment: 56 pages, comments welcome

Pattern Recognition: Industry seeking regulation – the case of crowdfunding. Bruges Political Research Papers 79/2020

At first it seems counterintuitive that an industry would seek regulation over itself, but from the point of view of crowdfunding, it was a logical step. Crowdfunding, as part of FinTech, is changing and challenging traditional financial institutions. The fragmentation of the EU market by national legislation on crowdfunding hindered its growth, and although FinTech is a diffuse interest, crowdfunding, as a pragmatic diffuse interest, formed legitimacy coalitions with the regulators. Utilizing Trumbull’s framework on pragmatic diffuse interest, my aim is to demonstrate through this case study that the industry lobby had influenced the agenda-setting and the policy-shaping, but only to the extent that there wasn’t conflicting interest from consumer groups. This is in line with previous finding on financial industry lobbying and some preliminary findings emerge, although as the proposal is still in first reading stage, the end results and conclusions remains to be see

Modal Empiricism and Two-Dimensional Semantics

In the paper I argue that it follows from David Chalmers’ semantics and metaphysics concerning microphysical terms that microphysical identifications are strongly necessary. This result supports modal empiricism and also counts in favour of a posteriori materialism (and thus against Chalmers’ property dualism), for it blocks the conjecture that a posteriori materialism is committed to strong necessities, but there are no such modalities