Search results for "Transcendence degree"

showing 2 items of 2 documents

Formal Periods and the Period Conjecture

2017

Following Kontsevich (see Kontsevich in Operads and motives in deformation quantization. Lett. Math. Phys. 48(1):35–72, 1999), we now introduce another algebra \(\tilde{\mathbb {P}}(k)\) of formal periods from the same data we have used in order to define the actual period algebra of a field in Chap. 11. The main aim of this chapter is to give conceptual interpretation of this algebra of formal periods. We then use it to formulate and discuss the period conjecture.

Discrete mathematicsHodge conjectureConjectureInterpretation (logic)Order (ring theory)Field (mathematics)Transcendence degreeHodge structurePeriod (music)Mathematics
researchProduct

Free differential Galois groups

2019

We study the structure of the absolute differential Galois group of a rational function field over an algebraically closed field of characteristic zero. In particular, we relate the behavior of differential embedding problems to the condition that the absolute differential Galois group is free as a proalgebraic group. Building on this, we prove Matzat's freeness conjecture in the case that the field of constants is algebraically closed of countably infinite transcendence degree over the rationals. This is the first known case of the twenty year old conjecture.

Rational numberPure mathematicsGroup (mathematics)Applied MathematicsGeneral Mathematics010102 general mathematicsGalois groupField (mathematics)Transcendence degreeMathematics - Commutative AlgebraCommutative Algebra (math.AC)01 natural sciences12H05 12F12 34M50FOS: MathematicsDifferential algebra0101 mathematicsAlgebraically closed fieldPicard–Vessiot theoryMathematics
researchProduct