Algebraic geometryAlgebraic geometry is a branch of mathematics which classically studies zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations.
Spirit (rover)Spirit, also known as MER-A (Mars Exploration Rover – A) or MER-2, is a Mars robotic rover, active from 2004 to 2010. Spirit was operational on Mars for sols or 3.3 Martian years ( days; ). It was one of two rovers of NASA's Mars Exploration Rover Mission managed by the Jet Propulsion Laboratory (JPL). Spirit landed successfully within the impact crater Gusev on Mars at 04:35 Ground UTC on January 4, 2004, three weeks before its twin, Opportunity (MER-B), which landed on the other side of the planet.
Mars Exploration RoverNASA's Mars Exploration Rover (MER) mission was a robotic space mission involving two Mars rovers, Spirit and Opportunity, exploring the planet Mars. It began in 2003 with the launch of the two rovers to explore the Martian surface and geology; both landed on Mars at separate locations in January 2004. Both rovers far outlived their planned missions of 90 Martian solar days: MER-A Spirit was active until March 22, 2010, while MER-B Opportunity was active until June 10, 2018.
Opportunity (rover)Opportunity, also known as MER-B (Mars Exploration Rover – B) or MER-1, is a robotic rover that was active on Mars from 2004 until 2018. Opportunity was operational on Mars for sols ( on Earth). Launched on July 7, 2003, as part of NASA's Mars Exploration Rover program, it landed in Meridiani Planum on January 25, 2004, three weeks after its twin, Spirit (MER-A), touched down on the other side of the planet. With a planned 90-sol duration of activity (slightly less than 92.
Derived algebraic geometryDerived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local charts, are replaced by either differential graded algebras (over ), simplicial commutative rings or -ring spectra from algebraic topology, whose higher homotopy groups account for the non-discreteness (e.g., Tor) of the structure sheaf. Grothendieck's scheme theory allows the structure sheaf to carry nilpotent elements.