26 research outputs found
Local Oort groups and the isolated differential data criterion
No full textIt is conjectured that if k is an algebraically closed field of
characteristic p > 0, then any branched G-cover of smooth projective k-curves
where the "KGB" obstruction vanishes and where a p-Sylow subgroup of G is
cyclic lifts to characteristic 0. Obus has shown that this conjecture holds
given the existence of certain meromorphic differential forms on P_1^k with
behavior determined by the ramification data of the cover. We give a more
efficient computational procedure to compute these forms than was previously
known. As a consequence, we show that all D_25- and D_27-covers lift to
characteristic zero.Comment: Minor edits, still 16 page
The (local) lifting problem for curves
No full textThe lifting problem that we consider asks: given a smooth curve in characteristic p and a group of automorphisms, can we lift the curve, along with the automorphisms, to characteristic zero? One can reduce this to a local question (the so-called local lifting problem) involving continuous group actions on formal power series rings. In this expos-itory article, we overview much of the progress that has been made toward determining when the local lifting problem has a solution, and we give a taste of the work currently being undertaken. Of particular interest is the case when the group of automorphisms is cyclic. In this case the lifting problem is expected to be solvable—this is the Oort conjecture. Content
Ramification of primes in fields of moduli of three -point covers
No full textWe examine in detail the stable reduction of three-point G-Galois covers of the projective line over a complete discrete valuation field of mixed characteristic (0, p), where G has a cyclic p-Sylow subgroup. In particular, we obtain results about ramification of primes in the minimal field of definition of the stable model of such a cover, under certain additional assumptions on G (one such sufficient, but not necessary set of assumptions is that G is solvable and p ≠ 2). This has the following consequence: Suppose f : Y → [special characters omitted] is a three-point G-Galois cover defined over [special characters omitted], where G has a cyclic p-Sylow subgroup of order pn, and these additional assumptions on G are satisfied. Then the nth higher ramification groups above p for the upper numbering for the extension [special characters omitted] vanish, where K is the field of moduli of f
Wild tame-by-cyclic extensions
No full textAbstractSuppose G is a semi-direct product of the form Z/pn⋊Z/m where p is prime and m is relatively prime to p. Suppose K is a complete discrete valuation field of characteristic p>0 with algebraically closed residue field. The main result states necessary and sufficient conditions on the ramification filtrations that occur for wildly ramified G-Galois extensions of K. In addition, we prove that there exists a parameter space for G-Galois extensions of K with given ramification filtration, and we calculate its dimension in terms of the ramification filtration. We provide explicit equations for wild cyclic extensions of K of degree p3
Bajji on the Beach: Middle-Class Food Practices in Chennai’s New Beach
No full textThis book produced by a group of interdisciplinary and international researchers working on a wide variety of cities throughout Asia, Latin America and Europe, addresses, rethinks and, in some cases, abandons the notions of formal and ..
